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
89.2-a1
89.2-a
$2$
$5$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
89.2
\( 89 \)
\( 89^{5} \)
$0.77630$
$(-7a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.2
$1$
\( 1 \)
$1$
$1.342664561$
0.474703608
\( -\frac{2723579700424704}{5584059449} a - \frac{3849798290264064}{5584059449} \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -19 a - 11\) , \( -15 a - 70\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-19a-11\right){x}-15a-70$
89.2-a2
89.2-a
$2$
$5$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
89.2
\( 89 \)
\( 89 \)
$0.77630$
$(-7a-3)$
0
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$5$
5B.1.1
$1$
\( 1 \)
$1$
$33.56661404$
0.474703608
\( \frac{2985984}{89} a - \frac{4091904}{89} \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( a - 1\) , \( -a\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}-a$
89.2-b1
89.2-b
$2$
$3$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
89.2
\( 89 \)
\( 89 \)
$0.77630$
$(-7a-3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$20.11509744$
0.790195656
\( -\frac{152338432}{89} a - \frac{215515136}{89} \)
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -2 a - 3\) , \( a + 1\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-2a-3\right){x}+a+1$
89.2-b2
89.2-b
$2$
$3$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
89.2
\( 89 \)
\( 89^{3} \)
$0.77630$
$(-7a-3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 1 \)
$1$
$2.235010827$
0.790195656
\( \frac{799366151176192}{704969} a - \frac{1130474448060416}{704969} \)
\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 18 a - 23\) , \( 59 a - 64\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(18a-23\right){x}+59a-64$
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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.