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
1369.1-a1
1369.1-a
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1369.1
\( 37^{2} \)
\( 37^{2} \)
$3.95710$
$(-2a+5), (2a+3)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 1 \)
$0.406699548$
$35.84317866$
8.009442048
\( \frac{110592}{37} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}$
1369.1-b1
1369.1-b
$3$
$9$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1369.1
\( 37^{2} \)
\( 37^{6} \)
$3.95710$
$(-2a+5), (2a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1
$1$
\( 3^{2} \)
$1$
$4.739517032$
0.651022732
\( \frac{1404928000}{50653} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -23\) , \( -50\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-23{x}-50$
1369.1-b2
1369.1-b
$3$
$9$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1369.1
\( 37^{2} \)
\( 37^{2} \)
$3.95710$
$(-2a+5), (2a+3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$1$
$42.65565329$
0.651022732
\( \frac{4096000}{37} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-3{x}+1$
1369.1-b3
1369.1-b
$3$
$9$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1369.1
\( 37^{2} \)
\( 37^{2} \)
$3.95710$
$(-2a+5), (2a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.2
$9$
\( 1 \)
$1$
$0.526613003$
0.651022732
\( \frac{727057727488000}{37} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -1873\) , \( -31833\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-1873{x}-31833$
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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.