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-a4
23.2-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.2
\( 23 \)
\( - 23^{2} \)
$14.79438$
$(-a^4+3a^2+a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$625$
\( 2 \)
$1$
$0.317800341$
0.820765345
\( -\frac{1191520348048782872032188672054705939}{529} a^{4} + \frac{2181471229802177623677475441208246860}{529} a^{3} + \frac{2953649593612105912153638037483875591}{529} a^{2} - \frac{6028541812813127685001791606278142264}{529} a + \frac{1434132506958014181934752744337840202}{529} \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} - a^{3} + 5 a^{2} + 2 a - 3\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -4278 a^{4} + 3350 a^{3} + 17601 a^{2} - 8315 a - 15116\) , \( -209580 a^{4} + 154663 a^{3} + 874447 a^{2} - 386208 a - 735950\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+2a-3\right){x}^{2}+\left(-4278a^{4}+3350a^{3}+17601a^{2}-8315a-15116\right){x}-209580a^{4}+154663a^{3}+874447a^{2}-386208a-735950$
529.14-a4
529.14-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.14
\( 23^{2} \)
\( - 23^{8} \)
$20.24275$
$(-a^4+3a^2+a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$25$
\( 2^{2} \)
$1$
$6.997752932$
1.44581672
\( -\frac{1191520348048782872032188672054705939}{529} a^{4} + \frac{2181471229802177623677475441208246860}{529} a^{3} + \frac{2953649593612105912153638037483875591}{529} a^{2} - \frac{6028541812813127685001791606278142264}{529} a + \frac{1434132506958014181934752744337840202}{529} \)
\( \bigl[a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( -a^{4} - a^{3} + 3 a^{2} + 4 a - 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 3\) , \( -10566 a^{4} + 8933 a^{3} + 43749 a^{2} - 22250 a - 38813\) , \( 848205 a^{4} - 616448 a^{3} - 3613623 a^{2} + 1606180 a + 3073152\bigr] \)
${y}^2+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+3\right){y}={x}^{3}+\left(-a^{4}-a^{3}+3a^{2}+4a-1\right){x}^{2}+\left(-10566a^{4}+8933a^{3}+43749a^{2}-22250a-38813\right){x}+848205a^{4}-616448a^{3}-3613623a^{2}+1606180a+3073152$
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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.