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
2.1-a2
2.1-a
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
2.1
\( 2 \)
\( - 2^{2} \)
$1.12963$
$(-a+6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$25.42172449$
1.195737336
\( \frac{32125}{4} a + \frac{158187}{4} \)
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 8\) , \( -a - 8\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+8{x}-a-8$
16.5-a2
16.5-a
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
16.5
\( 2^{4} \)
\( - 2^{14} \)
$1.89980$
$(-a+6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$3.562112878$
$10.27635668$
3.443559771
\( \frac{32125}{4} a + \frac{158187}{4} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -916 a - 4411\) , \( -37061 a - 178450\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-916a-4411\right){x}-37061a-178450$
32.3-h2
32.3-h
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
32.3
\( 2^{5} \)
\( - 2^{14} \)
$2.25926$
$(-a+6), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.354829174$
$22.97376349$
3.067412879
\( \frac{32125}{4} a + \frac{158187}{4} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -20 a + 138\) , \( -153 a + 936\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-20a+138\right){x}-153a+936$
64.6-a2
64.6-a
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
64.6
\( 2^{6} \)
\( - 2^{20} \)
$2.68672$
$(-a+6)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$7.458691788$
$7.266481497$
5.098560907
\( \frac{32125}{4} a + \frac{158187}{4} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -30 a - 129\) , \( -315 a - 1505\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-30a-129\right){x}-315a-1505$
64.6-d2
64.6-d
$2$
$2$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
64.6
\( 2^{6} \)
\( - 2^{20} \)
$2.68672$
$(-a+6)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$8.987936888$
0.845513979
\( \frac{32125}{4} a + \frac{158187}{4} \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -12678 a + 73711\) , \( -1815474 a + 10557107\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-12678a+73711\right){x}-1815474a+10557107$
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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.