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-c2
8.1-c
$4$
$10$
3.3.733.1
$3$
$[3, 0]$
8.1
\( 2^{3} \)
\( 2^{14} \)
$3.42141$
$(a^2-6), (a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$25$
\( 2^{2} \)
$1$
$1.085655071$
1.002489625
\( \frac{1665938991796893}{32} a^{2} - \frac{3101455467224985}{16} a + \frac{2527951775111977}{16} \)
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 6\) , \( 0\) , \( -9319242867 a^{2} - 14148462393 a + 29606060477\) , \( -915329396489703 a^{2} - 1389651899205825 a + 2907886170331433\bigr] \)
${y}^2+\left(a^{2}-5\right){x}{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-9319242867a^{2}-14148462393a+29606060477\right){x}-915329396489703a^{2}-1389651899205825a+2907886170331433$
64.3-g4
64.3-g
$4$
$10$
3.3.733.1
$3$
$[3, 0]$
64.3
\( 2^{6} \)
\( 2^{26} \)
$4.83861$
$(a^2-6), (a^2+a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$25$
\( 2^{2} \)
$1$
$2.988899124$
2.759937701
\( \frac{1665938991796893}{32} a^{2} - \frac{3101455467224985}{16} a + \frac{2527951775111977}{16} \)
\( \bigl[a\) , \( 0\) , \( a^{2} - 4\) , \( -659 a^{2} - 138 a + 949\) , \( -8134 a^{2} - 32312 a + 48774\bigr] \)
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-659a^{2}-138a+949\right){x}-8134a^{2}-32312a+48774$
200.3-c4
200.3-c
$4$
$10$
3.3.733.1
$3$
$[3, 0]$
200.3
\( 2^{3} \cdot 5^{2} \)
\( 2^{14} \cdot 5^{6} \)
$5.85053$
$(a^2-6), (-a+3), (a^2+a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$1$
\( 2^{3} \cdot 5 \)
$0.527149029$
$12.02545365$
7.024317722
\( \frac{1665938991796893}{32} a^{2} - \frac{3101455467224985}{16} a + \frac{2527951775111977}{16} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1632961234741 a^{2} - 2479159622634 a + 5187712106049\) , \( -2123083287970233119 a^{2} - 3223262286357900198 a + 6744768118697518249\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-1632961234741a^{2}-2479159622634a+5187712106049\right){x}-2123083287970233119a^{2}-3223262286357900198a+6744768118697518249$
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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.