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
441.1-a1
441.1-a
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{2} \cdot 7^{16} \)
$1.15823$
$(-2a+1), (2a+1), (3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1.950960562$
$0.814020435$
1.122971671
\( -\frac{4354703137}{17294403} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \)
${y}^2+{x}{y}={x}^{3}-34{x}-217$
3087.1-h1
3087.1-h
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3087.1
\( 3^{2} \cdot 7^{3} \)
\( 3^{2} \cdot 7^{22} \)
$1.88394$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$0.651668904$
1.843198006
\( -\frac{4354703137}{17294403} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 136 a - 306\) , \( -4774 a + 5425\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(136a-306\right){x}-4774a+5425$
3087.2-h1
3087.2-h
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3087.2
\( 3^{2} \cdot 7^{3} \)
\( 3^{2} \cdot 7^{22} \)
$1.88394$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{5} \)
$1$
$0.651668904$
1.843198006
\( -\frac{4354703137}{17294403} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -136 a - 306\) , \( 4774 a + 5425\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-136a-306\right){x}+4774a+5425$
3969.1-b1
3969.1-b
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3969.1
\( 3^{4} \cdot 7^{2} \)
\( 3^{14} \cdot 7^{16} \)
$2.00611$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$1$
$1.217293980$
1.721513656
\( -\frac{4354703137}{17294403} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-306{x}+5859$
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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.