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-a3
23.3-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.3
\( 23 \)
\( - 23^{5} \)
$14.79438$
$(-a^4+a^3+3a^2-3a-2)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 5 \)
$1$
$1986.252133$
0.820765345
\( \frac{46971305784}{6436343} a^{4} - \frac{20963315451}{6436343} a^{3} - \frac{187181929672}{6436343} a^{2} + \frac{62971709137}{6436343} a + \frac{147346928834}{6436343} \)
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 4 a - 6\) , \( -2 a^{4} + 8 a^{2} - 4\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-2a^{4}+a^{3}+9a^{2}-4a-6\right){x}-2a^{4}+8a^{2}-4$
529.13-a3
529.13-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.13
\( 23^{2} \)
\( - 23^{11} \)
$20.24275$
$(-a^4+a^3+3a^2-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2 \)
$1$
$349.8876466$
1.44581672
\( \frac{46971305784}{6436343} a^{4} - \frac{20963315451}{6436343} a^{3} - \frac{187181929672}{6436343} a^{2} + \frac{62971709137}{6436343} a + \frac{147346928834}{6436343} \)
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{4} - 4 a^{2} + 3\) , \( -2 a^{4} + 6 a^{2} - 2 a - 4\) , \( 5 a^{4} + 3 a^{3} - 15 a^{2} - 10 a + 1\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-2a^{4}+6a^{2}-2a-4\right){x}+5a^{4}+3a^{3}-15a^{2}-10a+1$
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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.