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
89.1-b1
89.1-b
$2$
$3$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
89.1
\( 89 \)
\( 89^{3} \)
$0.77630$
$(-7a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$2.235010827$
0.790195656
\( -\frac{799366151176192}{704969} a - \frac{1130474448060416}{704969} \)
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -18 a - 23\) , \( -60 a - 64\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-18a-23\right){x}-60a-64$
1424.1-d1
1424.1-d
$2$
$3$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1424.1
\( 2^{4} \cdot 89 \)
\( 2^{12} \cdot 89^{3} \)
$1.55261$
$(a), (-7a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 1 \)
$1$
$4.767226678$
1.685469156
\( -\frac{799366151176192}{704969} a - \frac{1130474448060416}{704969} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -72 a - 93\) , \( 404 a + 413\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(-72a-93\right){x}+404a+413$
4361.4-a1
4361.4-a
$2$
$3$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4361.4
\( 7^{2} \cdot 89 \)
\( 7^{6} \cdot 89^{3} \)
$2.05390$
$(-2a+1), (-7a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 3 \)
$1$
$0.517222765$
0.548597587
\( -\frac{799366151176192}{704969} a - \frac{1130474448060416}{704969} \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -68 a - 65\) , \( 161 a - 899\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-68a-65\right){x}+161a-899$
4361.6-d1
4361.6-d
$2$
$3$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
4361.6
\( 7^{2} \cdot 89 \)
\( 7^{6} \cdot 89^{3} \)
$2.05390$
$(2a+1), (-7a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$3$
3B
$1$
\( 2 \)
$0.310068073$
$5.885722166$
2.580903736
\( -\frac{799366151176192}{704969} a - \frac{1130474448060416}{704969} \)
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -92 a + 111\) , \( -8616 a + 12237\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-92a+111\right){x}-8616a+12237$
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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.