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
13.1-a2
13.1-a
$2$
$2$
5.5.36497.1
$5$
$[5, 0]$
13.1
\( 13 \)
\( 13^{2} \)
$22.06284$
$(a^3-3a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$568.2325455$
1.48719366
\( \frac{1596793}{169} a^{4} - \frac{937970}{169} a^{3} - \frac{7191975}{169} a^{2} + \frac{918304}{169} a + \frac{2080992}{169} \)
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( -a^{2} + 2 a + 1\) , \( a^{2} - a - 2\) , \( 4 a^{4} - 6 a^{3} - 13 a^{2} + 10 a + 6\) , \( 5 a^{4} - 4 a^{3} - 19 a^{2} + 2 a + 3\bigr] \)
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(4a^{4}-6a^{3}-13a^{2}+10a+6\right){x}+5a^{4}-4a^{3}-19a^{2}+2a+3$
13.1-b2
13.1-b
$2$
$2$
5.5.36497.1
$5$
$[5, 0]$
13.1
\( 13 \)
\( 13^{2} \)
$22.06284$
$(a^3-3a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.003887395$
$22493.89263$
1.14428645
\( \frac{1596793}{169} a^{4} - \frac{937970}{169} a^{3} - \frac{7191975}{169} a^{2} + \frac{918304}{169} a + \frac{2080992}{169} \)
\( \bigl[1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 6 a + 2\) , \( 0\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 6 a - 3\) , \( 0\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(2a^{4}-3a^{3}-7a^{2}+6a+2\right){x}^{2}+\left(-2a^{4}+3a^{3}+7a^{2}-6a-3\right){x}$
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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.