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
16.1-a3
16.1-a
$6$
$8$
3.3.316.1
$3$
$[3, 0]$
16.1
\( 2^{4} \)
\( 2^{12} \)
$2.52156$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$235.8112230$
1.658177211
\( -\frac{29580655}{16} a^{2} + \frac{7825805}{8} a + \frac{62873277}{8} \)
\( \bigl[a\) , \( a^{2} + a - 4\) , \( 0\) , \( 5607 a^{2} - 2969 a - 23826\) , \( -340349 a^{2} + 180146 a + 1446179\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(5607a^{2}-2969a-23826\right){x}-340349a^{2}+180146a+1446179$
32.1-a6
32.1-a
$6$
$8$
3.3.316.1
$3$
$[3, 0]$
32.1
\( 2^{5} \)
\( 2^{12} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$72.47588334$
1.019271743
\( -\frac{29580655}{16} a^{2} + \frac{7825805}{8} a + \frac{62873277}{8} \)
\( \bigl[a\) , \( -a^{2} + a + 4\) , \( a\) , \( 1631309 a^{2} - 863479 a - 6931663\) , \( 1660636815 a^{2} - 879002600 a - 7056279211\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(1631309a^{2}-863479a-6931663\right){x}+1660636815a^{2}-879002600a-7056279211$
128.5-b2
128.5-b
$6$
$8$
3.3.316.1
$3$
$[3, 0]$
128.5
\( 2^{7} \)
\( 2^{24} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$42.72314196$
1.201682252
\( -\frac{29580655}{16} a^{2} + \frac{7825805}{8} a + \frac{62873277}{8} \)
\( \bigl[a^{2} + a - 2\) , \( -1\) , \( 0\) , \( 49066 a^{2} - 25967 a - 208480\) , \( 8640239 a^{2} - 4573418 a - 36713583\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}-{x}^{2}+\left(49066a^{2}-25967a-208480\right){x}+8640239a^{2}-4573418a-36713583$
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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.