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
65.1-a1 65.1-a $2$
$2$
3.3.169.1 $3$
$[3, 0]$
65.1
\( 5 \cdot 13 \)
\( 5 \cdot 13 \)
$2.32935$
$(-a+1), (-2a^2+3a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 1 \)
$0.194885731$
$115.5814743$
1.299529626
\( \frac{4431229}{65} a^{2} - \frac{828994}{13} a - \frac{14115071}{65} \)
\( \bigl[a + 1\) , \( 1\) , \( a^{2} - 3\) , \( -2 a^{2} - 2 a + 1\) , \( -4 a^{2} - 8 a - 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+{x}^{2}+\left(-2a^{2}-2a+1\right){x}-4a^{2}-8a-4$
65.1-a2 65.1-a $2$
$2$
3.3.169.1 $3$
$[3, 0]$
65.1
\( 5 \cdot 13 \)
\( - 5^{2} \cdot 13^{2} \)
$2.32935$
$(-a+1), (-2a^2+3a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2B $1$
\( 2^{2} \)
$0.097442865$
$57.79073718$
1.299529626
\( -\frac{3841895376406}{325} a^{2} + \frac{978828129687}{65} a + \frac{14027154899859}{325} \)
\( \bigl[a + 1\) , \( 1\) , \( a^{2} - 3\) , \( -2 a^{2} + 3 a + 1\) , \( -8 a^{2} - 6 a - 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+{x}^{2}+\left(-2a^{2}+3a+1\right){x}-8a^{2}-6a-3$
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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.
