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-a8
8.1-a
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( 2^{12} \)
$2.24645$
$(a), (-a+1)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2 \cdot 3 \)
$1$
$72.96934799$
0.684141088
\( \frac{19825}{16} a^{2} - \frac{24115}{8} a + \frac{15581}{8} \)
\( \bigl[a\) , \( -a^{2} - a + 4\) , \( a\) , \( -15155975 a^{2} + 8022315 a + 64399881\) , \( 50371899485 a^{2} - 26662681574 a - 214037280091\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-15155975a^{2}+8022315a+64399881\right){x}+50371899485a^{2}-26662681574a-214037280091$
32.1-b4
32.1-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
32.1
\( 2^{5} \)
\( 2^{12} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1$
$134.9748073$
1.898231533
\( \frac{19825}{16} a^{2} - \frac{24115}{8} a + \frac{15581}{8} \)
\( \bigl[a\) , \( a^{2} - a - 3\) , \( a\) , \( -4408566115 a^{2} + 2333527139 a + 18732616995\) , \( -249975088401133 a^{2} + 132315958909892 a + 1062179281647772\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-4408566115a^{2}+2333527139a+18732616995\right){x}-249975088401133a^{2}+132315958909892a+1062179281647772$
64.5-b2
64.5-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
64.5
\( 2^{6} \)
\( 2^{24} \)
$3.17696$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$0.067143677$
$64.77783205$
2.202066878
\( \frac{19825}{16} a^{2} - \frac{24115}{8} a + \frac{15581}{8} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 4\) , \( a^{2} + a - 2\) , \( -174648 a^{2} + 92448 a + 742111\) , \( -62136703 a^{2} + 32889994 a + 264027596\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-174648a^{2}+92448a+742111\right){x}-62136703a^{2}+32889994a+264027596$
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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.