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-a3
8.1-a
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( 2^{11} \)
$2.24645$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$9$
\( 1 \)
$1$
$5.405136888$
0.684141088
\( -\frac{596658698344264096415}{8} a^{2} + \frac{157910670855855346189}{4} a + \frac{1267643331281111416669}{4} \)
\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a\) , \( 696542 a^{2} - 368715 a - 2959749\) , \( 463057095 a^{2} - 245103850 a - 1967594769\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(696542a^{2}-368715a-2959749\right){x}+463057095a^{2}-245103850a-1967594769$
32.1-b5
32.1-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
32.1
\( 2^{5} \)
\( 2^{11} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 3 \)
$1$
$44.99160244$
1.898231533
\( -\frac{596658698344264096415}{8} a^{2} + \frac{157910670855855346189}{4} a + \frac{1267643331281111416669}{4} \)
\( \bigl[a\) , \( -a^{2} + 4\) , \( a^{2} - 2\) , \( 202613715 a^{2} - 107246802 a - 860934154\) , \( -2295401845649 a^{2} + 1214994254958 a + 9753485033640\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(202613715a^{2}-107246802a-860934154\right){x}-2295401845649a^{2}+1214994254958a+9753485033640$
64.5-b3
64.5-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
64.5
\( 2^{6} \)
\( 2^{23} \)
$3.17696$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2 \)
$0.805724135$
$32.38891602$
2.202066878
\( -\frac{596658698344264096415}{8} a^{2} + \frac{157910670855855346189}{4} a + \frac{1267643331281111416669}{4} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( 6093848 a^{2} - 3225569 a - 25893607\) , \( -11978839714 a^{2} + 6340598481 a + 50899773446\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(6093848a^{2}-3225569a-25893607\right){x}-11978839714a^{2}+6340598481a+50899773446$
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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.