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David White
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Is it possible to compute coeffientscoefficients of the formal group of an elliptic curve?

This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}=Spec(A)$, is there a way to compute coefficentscoefficients of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients are rational or at least analtyicanalytic function of our parametrization, though I am not making any headway. Can anyone enlighten me on this issue?

Edit: When considering the pullback of $Spec(L)\to \mathcal{M}_{FG}$ along $\mathcal{M}_{Ell}\to \mathcal{M}_{FG}$, we get $Spec(A[b_1, b_2, ...])$ so that the zero morphism should give us a map $Spec(A)\to Spec(L)$, which should be what we want. Computation of this map though, is not clear to me.

Is it possible to compute coeffients of the formal group of an elliptic curve?

This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}=Spec(A)$, is there a way to compute coefficents of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients are rational or at least analtyic function of our parametrization, though I am not making any headway. Can anyone enlighten me on this issue?

Edit: When considering the pullback of $Spec(L)\to \mathcal{M}_{FG}$ along $\mathcal{M}_{Ell}\to \mathcal{M}_{FG}$, we get $Spec(A[b_1, b_2, ...])$ so that the zero morphism should give us a map $Spec(A)\to Spec(L)$, which should be what we want. Computation of this map though, is not clear to me.

Is it possible to compute coefficients of the formal group of an elliptic curve?

This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}=Spec(A)$, is there a way to compute coefficients of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients are rational or at least analytic function of our parametrization, though I am not making any headway. Can anyone enlighten me on this issue?

Edit: When considering the pullback of $Spec(L)\to \mathcal{M}_{FG}$ along $\mathcal{M}_{Ell}\to \mathcal{M}_{FG}$, we get $Spec(A[b_1, b_2, ...])$ so that the zero morphism should give us a map $Spec(A)\to Spec(L)$, which should be what we want. Computation of this map though, is not clear to me.

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Pax
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This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}$$R\to \mathbb{A}^5_{\mathbb{Z}}=Spec(A)$, is there a way to compute coefficents of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients are rational or at least analtyic function of our parametrization, though I am not making any headway. Can anyone enlighten me on this issue?

Edit: When considering the pullback of $Spec(L)\to \mathcal{M}_{FG}$ along $\mathcal{M}_{Ell}\to \mathcal{M}_{FG}$, we get $Spec(A[b_1, b_2, ...])$ so that the zero morphism should give us a map $Spec(A)\to Spec(L)$, which should be what we want. Computation of this map though, is not clear to me.

This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}$, is there a way to compute coefficents of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients are rational or at least analtyic function of our parametrization, though I am not making any headway. Can anyone enlighten me on this issue?

This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}=Spec(A)$, is there a way to compute coefficents of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients are rational or at least analtyic function of our parametrization, though I am not making any headway. Can anyone enlighten me on this issue?

Edit: When considering the pullback of $Spec(L)\to \mathcal{M}_{FG}$ along $\mathcal{M}_{Ell}\to \mathcal{M}_{FG}$, we get $Spec(A[b_1, b_2, ...])$ so that the zero morphism should give us a map $Spec(A)\to Spec(L)$, which should be what we want. Computation of this map though, is not clear to me.

Source Link
Pax
  • 841
  • 6
  • 16

Is it possible to compute coeffients of the formal group of an elliptic curve?

This may be trivial but I cannot find it. Given an elliptic curve, $C$ over $R$ with chosen parametrization $R\to \mathbb{A}^5_{\mathbb{Z}}$, is there a way to compute coefficents of the associated formal group law, assuming this is enough information to coordinatize it. I would assume that the coefficients are rational or at least analtyic function of our parametrization, though I am not making any headway. Can anyone enlighten me on this issue?