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
16.4-a4
16.4-a
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
16.4
\( 2^{4} \)
\( 2^{5} \)
$2.52156$
$(a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$232.3326080$
1.633716289
\( \frac{112062878879}{2} a^{2} - \frac{315301616071}{2} a + 61790982411 \)
\( \bigl[a + 1\) , \( -a^{2} + a + 4\) , \( 0\) , \( 11635 a^{2} - 6160 a - 49441\) , \( -979527 a^{2} + 518475 a + 4162139\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(11635a^{2}-6160a-49441\right){x}-979527a^{2}+518475a+4162139$
32.5-a1
32.5-a
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
32.5
\( 2^{5} \)
\( 2^{5} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 1 \)
$1$
$33.81710489$
1.902360777
\( \frac{112062878879}{2} a^{2} - \frac{315301616071}{2} a + 61790982411 \)
\( \bigl[a^{2} - 3\) , \( a^{2} + a - 3\) , \( a + 1\) , \( 11637 a^{2} - 6160 a - 49447\) , \( 996638 a^{2} - 527538 a - 4234857\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(11637a^{2}-6160a-49447\right){x}+996638a^{2}-527538a-4234857$
128.3-b3
128.3-b
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.3
\( 2^{7} \)
\( 2^{17} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$12.58523226$
1.415949254
\( \frac{112062878879}{2} a^{2} - \frac{315301616071}{2} a + 61790982411 \)
\( \bigl[a^{2} + a - 2\) , \( a + 1\) , \( 0\) , \( 224 a^{2} - 107 a - 934\) , \( 2719 a^{2} - 1426 a - 11531\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(224a^{2}-107a-934\right){x}+2719a^{2}-1426a-11531$
128.7-b2
128.7-b
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.7
\( 2^{7} \)
\( 2^{11} \)
$3.56602$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$38.23073087$
1.075323318
\( \frac{112062878879}{2} a^{2} - \frac{315301616071}{2} a + 61790982411 \)
\( \bigl[a^{2} - 3\) , \( -a^{2} - a + 4\) , \( a^{2} - 3\) , \( 34420 a^{2} - 18220 a - 146255\) , \( -5017146 a^{2} + 2655658 a + 21318558\bigr] \)
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(34420a^{2}-18220a-146255\right){x}-5017146a^{2}+2655658a+21318558$
128.7-e3
128.7-e
$4$
$4$
3.3.316.1
$3$
$[3, 0]$
128.7
\( 2^{7} \)
\( 2^{11} \)
$3.56602$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$0.229099761$
$102.7552442$
1.986444107
\( \frac{112062878879}{2} a^{2} - \frac{315301616071}{2} a + 61790982411 \)
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( 0\) , \( 34422 a^{2} - 18218 a - 146260\) , \( 5051567 a^{2} - 2673877 a - 21464816\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(34422a^{2}-18218a-146260\right){x}+5051567a^{2}-2673877a-21464816$
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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.