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
2916.1-a1
2916.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2916.1
\( 2^{2} \cdot 3^{6} \)
\( 2^{4} \cdot 3^{12} \)
$1.13736$
$(-2a+1), (2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 2 \cdot 3 \)
$0.305934883$
$3.305583379$
1.556987840
\( -\frac{35937}{4} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 8\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6{x}+8$
2916.1-a2
2916.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2916.1
\( 2^{2} \cdot 3^{6} \)
\( 2^{12} \cdot 3^{8} \)
$1.13736$
$(-2a+1), (2)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 2 \cdot 3^{2} \)
$0.101978294$
$3.305583379$
1.556987840
\( \frac{109503}{64} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+4{x}-1$
2916.1-b1
2916.1-b
$4$
$21$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2916.1
\( 2^{2} \cdot 3^{6} \)
\( 2^{14} \cdot 3^{12} \)
$1.13736$
$(-2a+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 7$
3B.1.1[2] , 7B.2.3
$1$
\( 3 \cdot 7 \)
$1$
$0.583485219$
1.572084960
\( -\frac{189613868625}{128} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -1077\) , \( 13877\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-1077{x}+13877$
2916.1-b2
2916.1-b
$4$
$21$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2916.1
\( 2^{2} \cdot 3^{6} \)
\( 2^{6} \cdot 3^{8} \)
$1.13736$
$(-2a+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 7$
3B.1.1[2] , 7B.2.1
$1$
\( 3 \)
$1$
$4.084396538$
1.572084960
\( -\frac{140625}{8} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-5{x}+5$
2916.1-b3
2916.1-b
$4$
$21$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2916.1
\( 2^{2} \cdot 3^{6} \)
\( 2^{42} \cdot 3^{8} \)
$1.13736$
$(-2a+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 7$
3B.1.1[2] , 7B.2.3
$1$
\( 3 \cdot 7 \)
$1$
$0.583485219$
1.572084960
\( -\frac{1159088625}{2097152} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -697\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-95{x}-697$
2916.1-b4
2916.1-b
$4$
$21$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
2916.1
\( 2^{2} \cdot 3^{6} \)
\( 2^{2} \cdot 3^{12} \)
$1.13736$
$(-2a+1), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3, 7$
3B.1.1[2] , 7B.2.1
$1$
\( 3 \)
$1$
$4.084396538$
1.572084960
\( \frac{3375}{2} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 3\) , \( -1\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+3{x}-1$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.