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
8281.3-CMe1
8281.3-CMe
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
8281.3
\( 7^{2} \cdot 13^{2} \)
\( 7^{10} \cdot 13^{8} \)
$1.47645$
$(-3a+1), (4a-3)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$7$
7Cs.2.1
$1$
\( 3 \)
$1$
$0.501915664$
1.738686864
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( a\) , \( -933 a + 1143\bigr] \)
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}-933a+1143$
8281.3-CMd1
8281.3-CMd
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
8281.3
\( 7^{2} \cdot 13^{2} \)
\( 7^{10} \cdot 13^{2} \)
$1.47645$
$(-3a+1), (4a-3)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$1$
\( 1 \)
$1$
$1.809682664$
2.089641546
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a\) , \( -4 a + 24\bigr] \)
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-4a+24$
8281.3-CMc1
8281.3-CMc
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
8281.3
\( 7^{2} \cdot 13^{2} \)
\( 7^{6} \cdot 13^{10} \)
$1.47645$
$(-3a+1), (4a-3)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$13$
13Cs.5.1
$1$
\( 2^{2} \)
$1$
$0.626142050$
2.892026252
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a\) , \( 191 a + 421\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+191a+421$
8281.3-CMb1
8281.3-CMb
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
8281.3
\( 7^{2} \cdot 13^{2} \)
\( 7^{6} \cdot 13^{4} \)
$1.47645$
$(-3a+1), (4a-3)$
$2$
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$7, 13$
7Cs.2.1 , 13Cs.5.1
$1$
\( 2^{2} \cdot 3 \)
$0.011943532$
$2.257587269$
1.494472576
\( 0 \)
\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a\) , \( 11 a\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}+11a$
8281.3-CMa1
8281.3-CMa
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
8281.3
\( 7^{2} \cdot 13^{2} \)
\( 7^{2} \cdot 13^{6} \)
$1.47645$
$(-3a+1), (4a-3)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$7$
7Cs.6.1
$1$
\( 1 \)
$1$
$2.816350280$
3.252041185
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( a\) , \( 5 a - 6\bigr] \)
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+5a-6$
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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.