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
23.5-a2
23.5-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.5
\( 23 \)
\( - 23^{5} \)
$14.79438$
$(a^2-a-3)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 5 \)
$1$
$1986.252133$
0.820765345
\( -\frac{20260021987}{6436343} a^{4} - \frac{26007990333}{6436343} a^{3} + \frac{59995009713}{6436343} a^{2} + \frac{98987286450}{6436343} a + \frac{35417701239}{6436343} \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 5 a + 6\) , \( -a^{2} - a + 3\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-5\right){x}^{2}+\left(2a^{4}-3a^{3}-7a^{2}+5a+6\right){x}-a^{2}-a+3$
529.11-a2
529.11-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.11
\( 23^{2} \)
\( - 23^{11} \)
$20.24275$
$(a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2 \)
$1$
$349.8876466$
1.44581672
\( -\frac{20260021987}{6436343} a^{4} - \frac{26007990333}{6436343} a^{3} + \frac{59995009713}{6436343} a^{2} + \frac{98987286450}{6436343} a + \frac{35417701239}{6436343} \)
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a\) , \( a^{3} - 3 a + 1\) , \( -2 a^{4} + a^{3} + 10 a^{2} - 3 a - 12\) , \( 8 a^{4} - 9 a^{3} - 28 a^{2} + 24 a + 12\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(-2a^{4}+a^{3}+10a^{2}-3a-12\right){x}+8a^{4}-9a^{3}-28a^{2}+24a+12$
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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.