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1d
comment Can we deduce that all the real zeros of those $k^{th}$ derivatives are also simple?
I guess it should be possible to show that they are simple for $s<0$ when $\vert s \vert$ is sufficiently large, because $L(C,s)$ tends to $1$ quite quickly as $s\to \infty$ so $L(C,s)$ is quite well described for $s\to -\infty$ by the functional equation. But WHY are you asking this question ?
Jul
14
awarded  Nice Answer
Jul
9
comment Bloch Kato Exponential as formal lie group exponential
For elliptic curves it is in Silverman IV.5.
Jul
3
revised Is the leading Taylor coefficient at $s = 1$ of the $L$-series of an elliptic curve over $\mathbb{Q}$ positive, as predicted by BSD?
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Jul
3
comment Is the leading Taylor coefficient at $s = 1$ of the $L$-series of an elliptic curve over $\mathbb{Q}$ positive, as predicted by BSD?
Modular in particular Manin-Drinfeld shows that the ratio is rational, but I don't see how this can be used to prove that it is positive. Would be interesting though.
Jul
3
comment Is the leading Taylor coefficient at $s = 1$ of the $L$-series of an elliptic curve over $\mathbb{Q}$ positive, as predicted by BSD?
I don't think Kolyvagin can say anything about the sign of the L-value. His argument is prime-by-prime and for most primes the formula of BSD then holds. But that will always miss the sign it seems to me.
Jul
3
answered Is the leading Taylor coefficient at $s = 1$ of the $L$-series of an elliptic curve over $\mathbb{Q}$ positive, as predicted by BSD?
Jun
17
comment Probability that $n$ is coprime to both $m$ and $m+1$
and $C\approx 0.3226$.
Jun
10
answered kernel of isogeny becomes constant after base change
May
12
revised Main conjecture for elliptic curves invariant under a $\mathbb{Q}$-isogeny
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May
12
comment Main conjecture for elliptic curves invariant under a $\mathbb{Q}$-isogeny
Oh ! I didn't know this.
May
12
answered Main conjecture for elliptic curves invariant under a $\mathbb{Q}$-isogeny
Apr
11
comment $\mu$-invariant and Pontryagin dual of Selmer group of elliptic curves 2
Theorem 11.3.11
Apr
11
comment $\mu$-invariant and Pontryagin dual of Selmer group of elliptic curves 2
$H^1(\mu_p)$ is not just the class group is also contains the $p$-units modulo $p$-th powers and they get a $\mu=1$. Should be some where in cohomology of number fields but I don't have it in front of me.
Mar
31
comment Kernel of a 3-isogeny between two elliptic curves
sage and probably magma have implemented the algorithm to find the dual. Often a look at the isogeny class (e.g. in Cremona's tables) is enough, say because there are only two curves there.
Mar
30
comment Kernel of a 3-isogeny between two elliptic curves
It is easy to check that $\ker \varphi =\mu_3$ by checking that the dual isogeny has a rational $3$-torsion point in its kernel.
Mar
30
awarded  Yearling
Mar
19
comment What is exceptional about the prime numbers 2 and 3?
Define an odd number $n>1$ to be prime when for all odd $d$ with $1<d\leq \sqrt{n}$ the remainder is non-zero. Then 5 and 7 become "exceptional", too.
Mar
15
answered Anomalous elliptic curves over finite rings
Mar
14
comment On $x^3-y^2=1728 \text{ unit}$ in number fields
$\mathcal{O}^*_K$ modulo $6$-th powers is a finite group.