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
8.1-a4
8.1-a
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( 2^{10} \)
$2.24645$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B.1.2
$9$
\( 2 \)
$1$
$10.81027377$
0.684141088
\( -\frac{266664752495}{64} a^{2} + \frac{71121115277}{32} a + \frac{567573953693}{32} \)
\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( 43522 a^{2} - 23060 a - 184974\) , \( 7250072 a^{2} - 3837642 a - 30806682\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(43522a^{2}-23060a-184974\right){x}+7250072a^{2}-3837642a-30806682$
32.1-b6
32.1-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
32.1
\( 2^{5} \)
\( 2^{10} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2 \cdot 3 \)
$1$
$89.98320488$
1.898231533
\( -\frac{266664752495}{64} a^{2} + \frac{71121115277}{32} a + \frac{567573953693}{32} \)
\( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 2\) , \( 12663355 a^{2} - 6702927 a - 53808379\) , \( -35853515497 a^{2} + 18977860206 a + 152346626128\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(12663355a^{2}-6702927a-53808379\right){x}-35853515497a^{2}+18977860206a+152346626128$
64.5-b4
64.5-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
64.5
\( 2^{6} \)
\( 2^{22} \)
$3.17696$
$(a), (-a+1)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2Cs , 3B
$1$
\( 2^{2} \)
$0.402862067$
$129.5556641$
2.202066878
\( -\frac{266664752495}{64} a^{2} + \frac{71121115277}{32} a + \frac{567573953693}{32} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( 380868 a^{2} - 201594 a - 1618352\) , \( -187393203 a^{2} + 99190339 a + 796260073\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(380868a^{2}-201594a-1618352\right){x}-187393203a^{2}+99190339a+796260073$
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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.