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-a1
13.1-a
$2$
$2$
5.5.36497.1
$5$
$[5, 0]$
13.1
\( 13 \)
\( - 13^{4} \)
$22.06284$
$(a^3-3a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$284.1162727$
1.48719366
\( -\frac{8844242842144}{28561} a^{4} + \frac{3901184928560}{28561} a^{3} + \frac{38808172739465}{28561} a^{2} + \frac{2512399121799}{28561} a - \frac{7585403021016}{28561} \)
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 9 a + 4\) , \( a\) , \( 53 a^{4} - 87 a^{3} - 190 a^{2} + 191 a + 122\) , \( 579 a^{4} - 931 a^{3} - 2120 a^{2} + 2049 a + 1416\bigr] \)
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+a{y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+9a+4\right){x}^{2}+\left(53a^{4}-87a^{3}-190a^{2}+191a+122\right){x}+579a^{4}-931a^{3}-2120a^{2}+2049a+1416$
13.1-b1
13.1-b
$2$
$2$
5.5.36497.1
$5$
$[5, 0]$
13.1
\( 13 \)
\( - 13^{4} \)
$22.06284$
$(a^3-3a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.007774790$
$11246.94631$
1.14428645
\( -\frac{8844242842144}{28561} a^{4} + \frac{3901184928560}{28561} a^{3} + \frac{38808172739465}{28561} a^{2} + \frac{2512399121799}{28561} a - \frac{7585403021016}{28561} \)
\( \bigl[1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 6 a + 2\) , \( 0\) , \( 8 a^{4} - 12 a^{3} - 28 a^{2} + 24 a + 12\) , \( 10 a^{4} - 19 a^{3} - 39 a^{2} + 50 a + 43\bigr] \)
${y}^2+{x}{y}={x}^{3}+\left(2a^{4}-3a^{3}-7a^{2}+6a+2\right){x}^{2}+\left(8a^{4}-12a^{3}-28a^{2}+24a+12\right){x}+10a^{4}-19a^{3}-39a^{2}+50a+43$
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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.