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
39.1-d1
39.1-d
$2$
$2$
\(\Q(\sqrt{237}) \)
$2$
$[2, 0]$
39.1
\( 3 \cdot 13 \)
\( - 3^{3} \cdot 13^{3} \)
$3.43779$
$(-a-7), (-a+9)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 3^{2} \)
$1$
$5.716729918$
3.342073611
\( -\frac{8290352125}{19773} a + \frac{67959714500}{19773} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 277 a - 2079\) , \( 7107 a - 57625\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(277a-2079\right){x}+7107a-57625$
39.1-f1
39.1-f
$2$
$2$
\(\Q(\sqrt{237}) \)
$2$
$[2, 0]$
39.1
\( 3 \cdot 13 \)
\( - 3^{3} \cdot 13^{3} \)
$3.43779$
$(-a-7), (-a+9)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 3 \)
$1.417588570$
$22.68731870$
3.133649804
\( -\frac{8290352125}{19773} a + \frac{67959714500}{19773} \)
\( \bigl[1\) , \( -a\) , \( 0\) , \( a + 25\) , \( 6 a + 57\bigr] \)
${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(a+25\right){x}+6a+57$
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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.