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
441.1-a3 441.1-a $6$
$8$
\(\Q(\sqrt{13}) \) $2$
$[2, 0]$
441.1
\( 3^{2} \cdot 7^{2} \)
\( 3^{8} \cdot 7^{4} \)
$1.47645$
$(-a), (-a+1), (7)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2$
2Cs $1$
\( 2^{5} \)
$0.667863882$
$13.02432697$
2.412523609
\( \frac{7189057}{3969} \)
\( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^{3}-4{x}-1$
1323.1-m3 1323.1-m $6$
$8$
\(\Q(\sqrt{13}) \) $2$
$[2, 0]$
1323.1
\( 3^{3} \cdot 7^{2} \)
\( 3^{14} \cdot 7^{4} \)
$1.94312$
$(-a), (-a+1), (7)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$7.963525558$
2.208684594
\( \frac{7189057}{3969} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -4 a - 12\) , \( 4 a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-12\right){x}+4a+3$
1323.2-m3 1323.2-m $6$
$8$
\(\Q(\sqrt{13}) \) $2$
$[2, 0]$
1323.2
\( 3^{3} \cdot 7^{2} \)
\( 3^{14} \cdot 7^{4} \)
$1.94312$
$(-a), (-a+1), (7)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
$2$
2Cs $1$
\( 2^{4} \)
$1$
$7.963525558$
2.208684594
\( \frac{7189057}{3969} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 4 a - 16\) , \( -4 a + 7\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(4a-16\right){x}-4a+7$
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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.
