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
77841.3-CMc1 77841.3-CMc $2$
$3$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
77841.3
\( 3^{4} \cdot 31^{2} \)
\( 3^{12} \cdot 31^{6} \)
$2.58524$
$(-2a+1), (6a-5)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$ ✓
✓
$3, 31$
3Cs[2] , 31Cs.7.1 $1$
\( 2^{2} \)
$1$
$0.840825582$
3.883607009
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -231 a + 14\bigr] \) ${y}^2+{y}={x}^{3}-231a+14$
77841.3-CMc2 77841.3-CMc $2$
$3$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
77841.3
\( 3^{4} \cdot 31^{2} \)
\( 3^{4} \cdot 31^{6} \)
$2.58524$
$(-2a+1), (6a-5)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-27$
$\mathrm{U}(1)$ ✓
✓
$31$
31Cs.7.1 $1$
\( 2^{2} \)
$1$
$0.840825582$
3.883607009
\( -12288000 \)
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 351 a - 240\) , \( 2011 a + 63\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(351a-240\right){x}+2011a+63$
77841.3-CMb1 77841.3-CMb $1$
$1$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
77841.3
\( 3^{4} \cdot 31^{2} \)
\( 3^{12} \cdot 31^{2} \)
$2.58524$
$(-2a+1), (6a-5)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$ ✓
✓
$31$
31Cs.7.1 $1$
\( 1 \)
$1$
$2.641353215$
3.049971979
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 3 a + 5\bigr] \) ${y}^2+{y}={x}^{3}+3a+5$
77841.3-CMa1 77841.3-CMa $1$
$1$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
77841.3
\( 3^{4} \cdot 31^{2} \)
\( 3^{6} \cdot 31^{8} \)
$2.58524$
$(-2a+1), (6a-5)$
0
$\Z/3\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$ ✓
✓
$3$
3B.1.1[2] $1$
\( 3 \)
$1$
$0.821686707$
0.316267361
\( 0 \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 276 a - 114\bigr] \) ${y}^2+{y}={x}^{3}+276a-114$
77841.3-a1 77841.3-a $1$
$1$
\(\Q(\sqrt{-3}) \) $2$
$[0, 1]$
77841.3
\( 3^{4} \cdot 31^{2} \)
\( 3^{10} \cdot 31^{8} \)
$2.58524$
$(-2a+1), (6a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$ $2$
2Cn $1$
\( 2^{2} \)
$0.614294300$
$0.517271645$
2.935313648
\( \frac{2138112}{961} a + \frac{5738496}{961} \)
\( \bigl[0\) , \( 0\) , \( 1\) , \( -243 a + 249\) , \( -108 a - 1251\bigr] \) ${y}^2+{y}={x}^{3}+\left(-243a+249\right){x}-108a-1251$
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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.
