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
1764.2-b2 1764.2-b $4$
$6$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
1764.2
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \)
$1.63798$
$(a), (-a-1), (a-1), (7)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B.1.1 $1$
\( 2 \cdot 3^{3} \)
$0.584118821$
$2.617295530$
3.243099107
\( \frac{2048000}{1323} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 7\) , \( 0\bigr] \) ${y}^2={x}^{3}+{x}^{2}+7{x}$
7056.2-c2 7056.2-c $4$
$6$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
7056.2
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{6} \cdot 7^{4} \)
$2.31645$
$(a), (-a-1), (a-1), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B $1$
\( 2^{2} \)
$1$
$2.617295530$
1.850707417
\( \frac{2048000}{1323} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}^{2}+7{x}$
15876.3-b2 15876.3-b $4$
$6$
\(\Q(\sqrt{-2}) \) $2$
$[0, 1]$
15876.3
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{18} \cdot 7^{4} \)
$2.83706$
$(a), (-a-1), (a-1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B.1.2 $1$
\( 2^{3} \)
$2.050203225$
$0.872431843$
5.059101756
\( \frac{2048000}{1323} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 60\) , \( 61\bigr] \) ${y}^2={x}^{3}+60{x}+61$
Download
displayed columns for
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.
