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Carl
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BSD conjecture for X_0(17)

I use Magma to calculate the L-value, yields

E:=EllipticCurve([1, -1, 1, -1, 0]); E; Evaluate(LSeries(E),1),RealPeriod(E),Evaluate(LSeries(E),1)/RealPeriod(E);

Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 - x over Rational Field 0.386769938387780043302394751243 3.09415950710224034641915800995 0.125000000000000000000000000000

$#torsionsubgroup = 4, c_{17}(E)=1.$

But the strong BSD predicts that

$L(E,1)/\Omega_{\infty}$= $(#Sha(E)/#tor(E)^2)*c_{17}(E)$

We will get $L(E,1)/\Omega_{\infty}=1/16$, not $1/8$. Why does that happen? Thanks a lot.

Carl
  • 73
  • 4