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
1369.2-a1
1369.2-a
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1369.2
\( 37^{2} \)
\( 37^{2} \)
$0.94146$
$(-7a+4), (-7a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 1 \)
$0.051111408$
$7.338132740$
0.866169275
\( \frac{110592}{37} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}$
1369.2-b1
1369.2-b
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1369.2
\( 37^{2} \)
\( 37^{10} \)
$0.94146$
$(-7a+4), (-7a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 3^{2} \)
$0.724769861$
$0.641360794$
1.073499626
\( -\frac{598618444955648000}{129961739795077} a + \frac{664724977577984000}{129961739795077} \)
\( \bigl[0\) , \( -a\) , \( 1\) , \( 157 a - 27\) , \( -90 a - 543\bigr] \)
${y}^2+{y}={x}^{3}-a{x}^{2}+\left(157a-27\right){x}-90a-543$
1369.2-b2
1369.2-b
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1369.2
\( 37^{2} \)
\( 37^{10} \)
$0.94146$
$(-7a+4), (-7a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 3^{2} \)
$0.724769861$
$0.641360794$
1.073499626
\( \frac{598618444955648000}{129961739795077} a + \frac{66106532622336000}{129961739795077} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -157 a + 130\) , \( 90 a - 633\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-157a+130\right){x}+90a-633$
1369.2-b3
1369.2-b
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1369.2
\( 37^{2} \)
\( 37^{6} \)
$0.94146$
$(-7a+4), (-7a+3)$
$1$
$\Z/3\Z\oplus\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3Cs.1.1[2]
$1$
\( 3^{2} \)
$2.174309583$
$1.924082382$
1.073499626
\( \frac{1404928000}{50653} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 23 a\) , \( -50\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+23a{x}-50$
1369.2-b4
1369.2-b
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1369.2
\( 37^{2} \)
\( 37^{2} \)
$0.94146$
$(-7a+4), (-7a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1[2]
$1$
\( 1 \)
$0.724769861$
$5.772247147$
1.073499626
\( \frac{4096000}{37} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 3 a\) , \( 1\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+3a{x}+1$
1369.2-b5
1369.2-b
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
1369.2
\( 37^{2} \)
\( 37^{2} \)
$0.94146$
$(-7a+4), (-7a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$3$
3B.1.1[2]
$1$
\( 1 \)
$6.522928749$
$0.641360794$
1.073499626
\( \frac{727057727488000}{37} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 1873 a\) , \( -31833\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+1873a{x}-31833$
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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.