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
576.1-e3 576.1-e $8$
$16$
\(\Q(\sqrt{3}, \sqrt{5})\) $4$
$[4, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{8} \)
$11.86705$
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$
$2$
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $1$
\( 2^{3} \)
$0.311730320$
$516.8363050$
5.370451569
\( \frac{3065617154}{9} \)
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} - \frac{5}{7} a^{2} - \frac{6}{7} a + \frac{26}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{2}{7} a^{3} + \frac{5373}{7} a^{2} - \frac{5395}{7} a - \frac{42340}{7}\) , \( \frac{1}{7} a^{3} - \frac{152808}{7} a^{2} + \frac{152797}{7} a + \frac{1203046}{7}\bigr] \) ${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){y}={x}^{3}+\left(\frac{1}{7}a^{3}-\frac{5}{7}a^{2}-\frac{6}{7}a+\frac{26}{7}\right){x}^{2}+\left(\frac{2}{7}a^{3}+\frac{5373}{7}a^{2}-\frac{5395}{7}a-\frac{42340}{7}\right){x}+\frac{1}{7}a^{3}-\frac{152808}{7}a^{2}+\frac{152797}{7}a+\frac{1203046}{7}$
576.1-n3 576.1-n $8$
$16$
\(\Q(\sqrt{3}, \sqrt{5})\) $4$
$[4, 0]$
576.1
\( 2^{6} \cdot 3^{2} \)
\( 2^{20} \cdot 3^{8} \)
$11.86705$
$(-2/7a^3+3/7a^2+19/7a-3/7), (-2/7a^3+3/7a^2+19/7a-10/7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2$
2B $16$
\( 2^{3} \)
$1$
$5.406926468$
2.883694116
\( \frac{3065617154}{9} \)
\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{9}{7}\) , \( 0\) , \( 769 a^{2} - 769 a - 6053\) , \( 22598 a^{2} - 22598 a - 177915\bigr] \) ${y}^2+\left(-\frac{2}{7}a^{3}+\frac{3}{7}a^{2}+\frac{19}{7}a-\frac{3}{7}\right){x}{y}={x}^{3}+\left(\frac{1}{7}a^{3}+\frac{2}{7}a^{2}-\frac{13}{7}a-\frac{9}{7}\right){x}^{2}+\left(769a^{2}-769a-6053\right){x}+22598a^{2}-22598a-177915$
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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.
