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
23.1-a2
23.1-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.1
\( 23 \)
\( - 23^{10} \)
$14.79438$
$(a^4-3a^2-1)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \cdot 5 \)
$1$
$993.1260669$
0.820765345
\( \frac{74868976618071917973}{41426511213649} a^{4} - \frac{54092178455960064989}{41426511213649} a^{3} - \frac{312961789930170680193}{41426511213649} a^{2} + \frac{134824139137681173208}{41426511213649} a + \frac{261494050662338262657}{41426511213649} \)
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 4 a - 4\) , \( a^{3} - 3 a + 1\) , \( -5 a^{4} + 7 a^{3} + 11 a^{2} - 3 a - 4\) , \( -a^{4} - 13 a^{3} + 27 a^{2} + 14 a - 8\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+4a-4\right){x}^{2}+\left(-5a^{4}+7a^{3}+11a^{2}-3a-4\right){x}-a^{4}-13a^{3}+27a^{2}+14a-8$
529.12-a2
529.12-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.12
\( 23^{2} \)
\( - 23^{16} \)
$20.24275$
$(a^4-3a^2-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{2} \)
$1$
$174.9438233$
1.44581672
\( \frac{74868976618071917973}{41426511213649} a^{4} - \frac{54092178455960064989}{41426511213649} a^{3} - \frac{312961789930170680193}{41426511213649} a^{2} + \frac{134824139137681173208}{41426511213649} a + \frac{261494050662338262657}{41426511213649} \)
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 1\) , \( -22 a^{4} + 30 a^{3} + 73 a^{2} - 39 a - 60\) , \( 51 a^{4} + 9 a^{3} - 325 a^{2} + 111 a + 301\bigr] \)
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-22a^{4}+30a^{3}+73a^{2}-39a-60\right){x}+51a^{4}+9a^{3}-325a^{2}+111a+301$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.