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 $3$
$9$
\(\Q(\sqrt{13}) \) $2$
$[2, 0]$
1369.1
\( 37^{2} \)
\( 37^{6} \)
$1.95980$
$(37)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3Cs.1.1 $1$
\( 3 \)
$3.159508490$
$4.739517032$
2.768794221
\( \frac{1404928000}{50653} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -23\) , \( -50\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-23{x}-50$
1369.1-a2 1369.1-a $3$
$9$
\(\Q(\sqrt{13}) \) $2$
$[2, 0]$
1369.1
\( 37^{2} \)
\( 37^{2} \)
$1.95980$
$(37)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3B.1.1 $1$
\( 1 \)
$1.053169496$
$42.65565329$
2.768794221
\( \frac{4096000}{37} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-3{x}+1$
1369.1-a3 1369.1-a $3$
$9$
\(\Q(\sqrt{13}) \) $2$
$[2, 0]$
1369.1
\( 37^{2} \)
\( 37^{2} \)
$1.95980$
$(37)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$3$
3B.1.2 $1$
\( 1 \)
$9.478525470$
$0.526613003$
2.768794221
\( \frac{727057727488000}{37} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -1873\) , \( -31833\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-1873{x}-31833$
1369.1-b1 1369.1-b $1$
$1$
\(\Q(\sqrt{13}) \) $2$
$[2, 0]$
1369.1
\( 37^{2} \)
\( 37^{2} \)
$1.95980$
$(37)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$1$
\( 1 \)
$0.051111408$
$35.84317866$
1.016208173
\( \frac{110592}{37} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}-{x}$
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Pari/GP
SageMath
Magma
Oscar
CSV
*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.
