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
37.1-a2
37.1-a
$3$
$9$
\(\Q(\sqrt{37}) \)
$2$
$[2, 0]$
37.1
\( 37 \)
\( 37^{2} \)
$1.34057$
$(-2a+1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B.1.1
$1$
\( 2 \)
$0.614182185$
$42.65565329$
1.914213755
\( \frac{4096000}{37} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}-3{x}+1$
333.2-c2
333.2-c
$3$
$9$
\(\Q(\sqrt{37}) \)
$2$
$[2, 0]$
333.2
\( 3^{2} \cdot 37 \)
\( 3^{6} \cdot 37^{2} \)
$2.32194$
$(a-3), (-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cn , 3B
$1$
\( 2 \)
$1$
$13.33043377$
4.383019626
\( \frac{4096000}{37} \)
\( \bigl[0\) , \( a\) , \( 1\) , \( 17 a - 57\) , \( 51 a - 180\bigr] \)
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(17a-57\right){x}+51a-180$
333.3-c2
333.3-c
$3$
$9$
\(\Q(\sqrt{37}) \)
$2$
$[2, 0]$
333.3
\( 3^{2} \cdot 37 \)
\( 3^{6} \cdot 37^{2} \)
$2.32194$
$(a+2), (-2a+1)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2Cn , 3B
$1$
\( 2 \)
$1$
$13.33043377$
4.383019626
\( \frac{4096000}{37} \)
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -17 a - 40\) , \( -51 a - 129\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-17a-40\right){x}-51a-129$
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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.