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-a2
23.3-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.3
\( 23 \)
\( - 23^{10} \)
$14.79438$
$(-a^4+a^3+3a^2-3a-2)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \cdot 5 \)
$1$
$993.1260669$
0.820765345
\( \frac{13485883457883008301}{41426511213649} a^{4} - \frac{40938279688082030060}{41426511213649} a^{3} + \frac{13634528082311040086}{41426511213649} a^{2} + \frac{34459978988291163906}{41426511213649} a - \frac{9914142943608711568}{41426511213649} \)
\( \bigl[a^{4} - 3 a^{2}\) , \( -a^{4} + a^{3} + 4 a^{2} - 4 a - 2\) , \( a^{4} - 3 a^{2} + a + 1\) , \( 18 a^{4} - 30 a^{3} - 46 a^{2} + 82 a - 17\) , \( -37 a^{4} + 76 a^{3} + 93 a^{2} - 205 a + 49\bigr] \)
${y}^2+\left(a^{4}-3a^{2}\right){x}{y}+\left(a^{4}-3a^{2}+a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-4a-2\right){x}^{2}+\left(18a^{4}-30a^{3}-46a^{2}+82a-17\right){x}-37a^{4}+76a^{3}+93a^{2}-205a+49$
529.13-a2
529.13-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.13
\( 23^{2} \)
\( - 23^{16} \)
$20.24275$
$(-a^4+a^3+3a^2-3a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{2} \)
$1$
$174.9438233$
1.44581672
\( \frac{13485883457883008301}{41426511213649} a^{4} - \frac{40938279688082030060}{41426511213649} a^{3} + \frac{13634528082311040086}{41426511213649} a^{2} + \frac{34459978988291163906}{41426511213649} a - \frac{9914142943608711568}{41426511213649} \)
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{4} - 4 a^{2} + 3\) , \( 23 a^{4} + 20 a^{3} - 94 a^{2} - 57 a + 16\) , \( 140 a^{4} + 24 a^{3} - 462 a^{2} - 205 a + 95\bigr] \)
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(23a^{4}+20a^{3}-94a^{2}-57a+16\right){x}+140a^{4}+24a^{3}-462a^{2}-205a+95$
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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.