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
4.1-e4
4.1-e
$4$
$6$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( 2^{19} \)
$1.34336$
$(-a+6), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$4.875328653$
$4.430022119$
2.031751412
\( \frac{223965069241}{262144} a + \frac{322827098891}{65536} \)
\( \bigl[1\) , \( a\) , \( 0\) , \( -2861 a - 13769\) , \( -197859 a - 952709\bigr] \)
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-2861a-13769\right){x}-197859a-952709$
32.3-f4
32.3-f
$4$
$6$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
32.3
\( 2^{5} \)
\( 2^{31} \)
$2.25926$
$(-a+6), (a+5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$9$
\( 2^{2} \)
$1$
$5.678332250$
4.807553080
\( \frac{223965069241}{262144} a + \frac{322827098891}{65536} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -a - 77\) , \( 22 a - 95\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-77\right){x}+22a-95$
32.4-b4
32.4-b
$4$
$6$
\(\Q(\sqrt{113}) \)
$2$
$[2, 0]$
32.4
\( 2^{5} \)
\( 2^{31} \)
$2.25926$
$(-a+6), (a+5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{3} \)
$1.101248121$
$4.796707197$
1.987692317
\( \frac{223965069241}{262144} a + \frac{322827098891}{65536} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -8060834 a - 38813488\) , \( -28743116176 a - 138400199932\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-8060834a-38813488\right){x}-28743116176a-138400199932$
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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.