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
23.3-a1
23.3-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.3
\( 23 \)
\( - 23^{2} \)
$14.79438$
$(-a^4+a^3+3a^2-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$625$
\( 2 \)
$1$
$0.317800341$
0.820765345
\( \frac{369039431219152047702358790473298695}{529} a^{4} - \frac{989950881753394751645286769153540921}{529} a^{3} + \frac{189441628332164246837405561968453764}{529} a^{2} + \frac{788381415458006631258384866252375903}{529} a - \frac{219339008287534382162591638591097088}{529} \)
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -32 a^{4} + 731 a^{3} - 356 a^{2} - 1659 a - 761\) , \( -179 a^{4} + 13981 a^{3} - 10713 a^{2} - 28326 a - 8289\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-32a^{4}+731a^{3}-356a^{2}-1659a-761\right){x}-179a^{4}+13981a^{3}-10713a^{2}-28326a-8289$
529.13-a1
529.13-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.13
\( 23^{2} \)
\( - 23^{8} \)
$20.24275$
$(-a^4+a^3+3a^2-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$25$
\( 2^{2} \)
$1$
$6.997752932$
1.44581672
\( \frac{369039431219152047702358790473298695}{529} a^{4} - \frac{989950881753394751645286769153540921}{529} a^{3} + \frac{189441628332164246837405561968453764}{529} a^{2} + \frac{788381415458006631258384866252375903}{529} a - \frac{219339008287534382162591638591097088}{529} \)
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{4} - 4 a^{2} + 3\) , \( -1537 a^{4} + 6825 a^{3} - 4314 a^{2} - 7437 a + 1156\) , \( 147589 a^{4} - 518205 a^{3} + 247122 a^{2} + 458708 a - 154955\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-1537a^{4}+6825a^{3}-4314a^{2}-7437a+1156\right){x}+147589a^{4}-518205a^{3}+247122a^{2}+458708a-154955$
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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.