Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
676.5-f1
676.5-f
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( 2^{12} \cdot 13^{8} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \cdot 5 \)
$1$
$0.889215470$
4.313328599
\( -\frac{7851401}{1024} a - \frac{3092357}{256} \)
\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 12 a - 46\) , \( 191 a - 523\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-46\right){x}+191a-523$
676.5-h1
676.5-h
$1$
$1$
\(\Q(\sqrt{17}) \)
$2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( 2^{12} \cdot 13^{2} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2^{2} \cdot 5 \)
$0.015453254$
$21.38066475$
3.205359110
\( -\frac{7851401}{1024} a - \frac{3092357}{256} \)
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( 5 a + 8\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a-8\right){x}+5a+8$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.