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-b1 676.5-b $2$
$2$
\(\Q(\sqrt{17}) \) $2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( - 2^{9} \cdot 13^{9} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2, 3$
2B , 3Ns $1$
\( 2^{2} \cdot 3 \)
$1$
$2.842831880$
2.068464020
\( -\frac{5924025}{64} a + \frac{15167717}{64} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 203 a - 520\) , \( -2201 a + 5631\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(203a-520\right){x}-2201a+5631$
676.5-d1 676.5-d $2$
$2$
\(\Q(\sqrt{17}) \) $2$
$[2, 0]$
676.5
\( 2^{2} \cdot 13^{2} \)
\( - 2^{9} \cdot 13^{3} \)
$1.87867$
$(-a+2), (-a-1), (2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ $2, 3$
2B , 3Ns $1$
\( 2^{2} \)
$0.353307593$
$10.12065257$
1.734470918
\( -\frac{5924025}{64} a + \frac{15167717}{64} \)
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -a - 3\) , \( 6 a + 6\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-a-3\right){x}+6a+6$
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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.
