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
36.2-a3
36.2-a
$4$
$6$
\(\Q(\sqrt{5}, \sqrt{13})\)
$4$
$[4, 0]$
36.2
\( 2^{2} \cdot 3^{2} \)
\( - 2^{4} \cdot 3^{12} \)
$9.09054$
$(1/2a^3-9/2a+1), (1/4a^3-11/4a+1/2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2^{2} \cdot 3 \)
$0.019604132$
$608.7739793$
2.203289626
\( \frac{11889835}{11664} a^{3} - \frac{14861959}{5832} a^{2} + \frac{203297}{11664} a + \frac{331277}{216} \)
\( \bigl[1\) , \( \frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{9}{4} a + \frac{5}{2}\) , \( a\) , \( a^{3} - \frac{5}{2} a^{2} - \frac{9}{2} a + 4\) , \( -\frac{3}{2} a^{3} + \frac{9}{2} a^{2} - a - 1\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{9}{4}a+\frac{5}{2}\right){x}^{2}+\left(a^{3}-\frac{5}{2}a^{2}-\frac{9}{2}a+4\right){x}-\frac{3}{2}a^{3}+\frac{9}{2}a^{2}-a-1$
324.3-b3
324.3-b
$4$
$6$
\(\Q(\sqrt{5}, \sqrt{13})\)
$4$
$[4, 0]$
324.3
\( 2^{2} \cdot 3^{4} \)
\( - 2^{4} \cdot 3^{24} \)
$11.96382$
$(1/2a^3-9/2a+1), (1/4a^3-11/4a+1/2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \)
$0.876850187$
$33.47463987$
3.612583906
\( \frac{11889835}{11664} a^{3} - \frac{14861959}{5832} a^{2} + \frac{203297}{11664} a + \frac{331277}{216} \)
\( \bigl[1\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{13}{4} a - \frac{5}{2}\) , \( \frac{1}{4} a^{3} - \frac{7}{4} a - \frac{1}{2}\) , \( -24 a^{3} - 66 a^{2} + 22 a + 38\) , \( -221 a^{3} - 646 a^{2} + 101 a + 301\bigr] \)
${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}-\frac{7}{4}a-\frac{1}{2}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+\frac{1}{2}a^{2}-\frac{13}{4}a-\frac{5}{2}\right){x}^{2}+\left(-24a^{3}-66a^{2}+22a+38\right){x}-221a^{3}-646a^{2}+101a+301$
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Pari/GP
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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.