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-a1
23.1-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.1
\( 23 \)
\( - 23^{5} \)
$14.79438$
$(a^4-3a^2-1)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 5 \)
$1$
$1986.252133$
0.820765345
\( -\frac{47053068568}{6436343} a^{4} + \frac{46268012320}{6436343} a^{3} + \frac{141240968488}{6436343} a^{2} - \frac{112796046627}{6436343} a + \frac{7676072842}{6436343} \)
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 4 a - 4\) , \( a^{3} - 3 a + 1\) , \( 2 a^{3} + a^{2} - 3 a + 1\) , \( 2 a^{4} - 4 a^{2} + a\bigr] \)
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+4a-4\right){x}^{2}+\left(2a^{3}+a^{2}-3a+1\right){x}+2a^{4}-4a^{2}+a$
529.12-a1
529.12-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.12
\( 23^{2} \)
\( - 23^{11} \)
$20.24275$
$(a^4-3a^2-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2 \)
$1$
$349.8876466$
1.44581672
\( -\frac{47053068568}{6436343} a^{4} + \frac{46268012320}{6436343} a^{3} + \frac{141240968488}{6436343} a^{2} - \frac{112796046627}{6436343} a + \frac{7676072842}{6436343} \)
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 1\) , \( 8 a^{4} + 5 a^{3} - 22 a^{2} - 9 a + 5\) , \( 4 a^{4} + 7 a^{3} - 7 a^{2} + a + 7\bigr] \)
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(8a^{4}+5a^{3}-22a^{2}-9a+5\right){x}+4a^{4}+7a^{3}-7a^{2}+a+7$
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.