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
23.4-a1
23.4-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.4
\( 23 \)
\( - 23^{2} \)
$14.79438$
$(-a^4+2a^2+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$625$
\( 2 \)
$1$
$0.317800341$
0.820765345
\( -\frac{1665599353208772437646840723861648544}{529} a^{4} - \frac{515871876593405186030634717346598316}{529} a^{3} + \frac{5986748941379712064585808940738486553}{529} a^{2} + \frac{2844175551769835948036386085428144797}{529} a - \frac{1271720281023855543211042033983127776}{529} \)
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a\) , \( -a^{4} - a^{3} + 5 a^{2} + 3 a - 5\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( -2681 a^{4} - 1331 a^{3} + 7125 a^{2} + 587 a - 4049\) , \( -146736 a^{4} - 108973 a^{3} + 354020 a^{2} + 126719 a - 132130\bigr] \)
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+3a-5\right){x}^{2}+\left(-2681a^{4}-1331a^{3}+7125a^{2}+587a-4049\right){x}-146736a^{4}-108973a^{3}+354020a^{2}+126719a-132130$
529.15-a1
529.15-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.15
\( 23^{2} \)
\( - 23^{8} \)
$20.24275$
$(-a^4+2a^2+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$25$
\( 2^{2} \)
$1$
$6.997752932$
1.44581672
\( -\frac{1665599353208772437646840723861648544}{529} a^{4} - \frac{515871876593405186030634717346598316}{529} a^{3} + \frac{5986748941379712064585808940738486553}{529} a^{2} + \frac{2844175551769835948036386085428144797}{529} a - \frac{1271720281023855543211042033983127776}{529} \)
\( \bigl[a^{2} - 1\) , \( -a^{4} + 5 a^{2} - a - 5\) , \( a^{3} - 3 a\) , \( -9701 a^{4} + 4825 a^{3} + 37011 a^{2} - 14694 a - 30397\) , \( 683650 a^{4} - 332513 a^{3} - 2681517 a^{2} + 978125 a + 2147146\bigr] \)
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-a-5\right){x}^{2}+\left(-9701a^{4}+4825a^{3}+37011a^{2}-14694a-30397\right){x}+683650a^{4}-332513a^{3}-2681517a^{2}+978125a+2147146$
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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.