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
23.2-a3
23.2-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.2
\( 23 \)
\( -23 \)
$14.79438$
$(-a^4+3a^2+a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$625$
\( 1 \)
$1$
$0.635600682$
0.820765345
\( \frac{13574836097602783212489}{23} a^{4} + \frac{12473814277431687078179}{23} a^{3} - \frac{30359946152158241249912}{23} a^{2} - \frac{17532655195108990218943}{23} a + \frac{7073167122009569142064}{23} \)
\( \bigl[a^{3} - 2 a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -187 a^{4} - 46 a^{3} + 506 a^{2} - 163 a - 437\) , \( -3375 a^{4} - 1423 a^{3} + 9018 a^{2} - 208 a - 5628\bigr] \)
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}^{2}+\left(-187a^{4}-46a^{3}+506a^{2}-163a-437\right){x}-3375a^{4}-1423a^{3}+9018a^{2}-208a-5628$
529.14-a3
529.14-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.14
\( 23^{2} \)
\( - 23^{7} \)
$20.24275$
$(-a^4+3a^2+a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$25$
\( 2 \)
$1$
$13.99550586$
1.44581672
\( \frac{13574836097602783212489}{23} a^{4} + \frac{12473814277431687078179}{23} a^{3} - \frac{30359946152158241249912}{23} a^{2} - \frac{17532655195108990218943}{23} a + \frac{7073167122009569142064}{23} \)
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( a^{4} + a^{3} - 3 a^{2} - 3 a - 1\) , \( a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( 47 a^{4} + 150 a^{3} - 160 a^{2} - 971 a - 874\) , \( -7241 a^{4} - 8629 a^{3} + 18825 a^{2} + 27489 a + 9832\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-3a^{2}-3a-1\right){x}^{2}+\left(47a^{4}+150a^{3}-160a^{2}-971a-874\right){x}-7241a^{4}-8629a^{3}+18825a^{2}+27489a+9832$
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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.