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-a7
8.1-a
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( 2^{20} \)
$2.24645$
$(a), (-a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$9$
\( 2 \)
$1$
$2.702568444$
0.684141088
\( \frac{532560105997425}{4096} a^{2} - \frac{749207151764755}{2048} a + \frac{293646661918461}{2048} \)
\( \bigl[a\) , \( -a^{2} - a + 4\) , \( a\) , \( 420286700 a^{2} - 222464805 a - 1785857409\) , \( 6903318103765 a^{2} - 3654040730844 a - 29333168803431\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(420286700a^{2}-222464805a-1785857409\right){x}+6903318103765a^{2}-3654040730844a-29333168803431$
32.1-b3
32.1-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
32.1
\( 2^{5} \)
\( 2^{20} \)
$2.83035$
$(a), (-a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$1$
$44.99160244$
1.898231533
\( \frac{532560105997425}{4096} a^{2} - \frac{749207151764755}{2048} a + \frac{293646661918461}{2048} \)
\( \bigl[a\) , \( a^{2} - a - 3\) , \( a\) , \( 122252877320 a^{2} - 64710474941 a - 519469656935\) , \( -34245221998777113 a^{2} + 18126563794145582 a + 145512761032249632\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(122252877320a^{2}-64710474941a-519469656935\right){x}-34245221998777113a^{2}+18126563794145582a+145512761032249632$
64.5-b1
64.5-b
$8$
$12$
3.3.316.1
$3$
$[3, 0]$
64.5
\( 2^{6} \)
\( 2^{32} \)
$3.17696$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$0.201431033$
$64.77783205$
2.202066878
\( \frac{532560105997425}{4096} a^{2} - \frac{749207151764755}{2048} a + \frac{293646661918461}{2048} \)
\( \bigl[a^{2} + a - 2\) , \( a^{2} - 4\) , \( a^{2} + a - 2\) , \( 4843162 a^{2} - 2563562 a - 20579269\) , \( -8544330873 a^{2} + 4522656004 a + 36306062696\bigr] \)
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(4843162a^{2}-2563562a-20579269\right){x}-8544330873a^{2}+4522656004a+36306062696$
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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.