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-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
\( \frac{727057727488000}{37} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 1873 a\) , \( -31833\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+1873a{x}-31833$
50653.2-b5
50653.2-b
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
50653.2
\( 37^{3} \)
\( 37^{8} \)
$2.32194$
$(-7a+4), (-7a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B[2]
$9$
\( 2^{2} \)
$1$
$0.105439065$
4.383019626
\( \frac{727057727488000}{37} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 61820 a - 74933\) , \( 7885109 a - 5673688\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+\left(61820a-74933\right){x}+7885109a-5673688$
50653.3-b5
50653.3-b
$5$
$9$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
50653.3
\( 37^{3} \)
\( 37^{8} \)
$2.32194$
$(-7a+4), (-7a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B[2]
$9$
\( 2^{2} \)
$1$
$0.105439065$
4.383019626
\( \frac{727057727488000}{37} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 74933 a - 61820\) , \( -7885109 a + 2211421\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(74933a-61820\right){x}-7885109a+2211421$
Download
displayed columns for
results
to
Text
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.