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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 ManinDrinfeld 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 Lvalue. His argument is primebyprime 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 3isogeny 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 3isogeny 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 nonzero. Then 5 and 7 become "exceptional", too. 
Mar 15 
answered  Anomalous elliptic curves over finite rings 
Mar 14 
comment 
On $x^3y^2=1728 \text{ unit}$ in number fields
$\mathcal{O}^*_K$ modulo $6$th powers is a finite group. 