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-a3
441.1-a
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{8} \cdot 7^{4} \)
$1.15823$
$(-2a+1), (2a+1), (3)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$0.487740140$
$13.02432697$
1.122971671
\( \frac{7189057}{3969} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \)
${y}^2+{x}{y}={x}^{3}-4{x}-1$
3087.1-h3
3087.1-h
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3087.1
\( 3^{2} \cdot 7^{3} \)
\( 3^{8} \cdot 7^{10} \)
$1.88394$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$5.213351238$
1.843198006
\( \frac{7189057}{3969} \)
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 16 a - 36\) , \( -22 a + 25\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(16a-36\right){x}-22a+25$
3087.2-h3
3087.2-h
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3087.2
\( 3^{2} \cdot 7^{3} \)
\( 3^{8} \cdot 7^{10} \)
$1.88394$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$5.213351238$
1.843198006
\( \frac{7189057}{3969} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -16 a - 36\) , \( 22 a + 25\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-16a-36\right){x}+22a+25$
3969.1-b3
3969.1-b
$6$
$8$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
3969.1
\( 3^{4} \cdot 7^{2} \)
\( 3^{20} \cdot 7^{4} \)
$2.00611$
$(-2a+1), (2a+1), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$4.869175922$
1.721513656
\( \frac{7189057}{3969} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}+27$
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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.