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
51.1-a1
51.1-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
51.1
\( 3 \cdot 17 \)
\( 3^{2} \cdot 17^{2} \)
$0.67542$
$(-a-1), (-2a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.032029606$
$7.122411322$
0.322621752
\( -\frac{1437952}{2601} a - \frac{95168}{2601} \)
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -a\) , \( 0\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-a{x}$
51.1-a2
51.1-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
51.1
\( 3 \cdot 17 \)
\( 3^{4} \cdot 17 \)
$0.67542$
$(-a-1), (-2a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.064059212$
$7.122411322$
0.322621752
\( \frac{4268288}{1377} a + \frac{2027584}{1377} \)
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -2 a + 2\) , \( 0\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+2\right){x}$
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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.