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-a1
37.1-a
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
37.1
\( 37 \)
\( 37 \)
$1.60445$
$(-2a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$14.86342269$
2.041648123
\( \frac{385513}{37} a - \frac{1668167}{37} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( a + 4\) , \( a + 3\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a+4\right){x}+a+3$
1369.2-b1
1369.2-b
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
1369.2
\( 37^{2} \)
\( 37^{7} \)
$3.95710$
$(-2a+5)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$1$
\( 2 \)
$1$
$3.499007833$
0.961251378
\( \frac{385513}{37} a - \frac{1668167}{37} \)
\( \bigl[1\) , \( -a\) , \( 1\) , \( 67 a - 275\) , \( -502 a + 2077\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(67a-275\right){x}-502a+2077$
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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.