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-a4
23.5-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.5
\( 23 \)
\( - 23^{2} \)
$14.79438$
$(a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$625$
\( 2 \)
$1$
$0.317800341$
0.820765345
\( \frac{675648471455377686001553954708107623}{529} a^{4} + \frac{620911450534242703942927978680242226}{529} a^{3} - \frac{1511073537772727871974027146777724553}{529} a^{2} - \frac{872783469849333360183497166887185757}{529} a + \frac{352086200751501274019816024338865057}{529} \)
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 5\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 247 a^{4} - 703 a^{3} - 792 a^{2} + 1375 a - 829\) , \( 3387 a^{4} - 14884 a^{3} - 12485 a^{2} + 30720 a - 11294\bigr] \)
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-4a-5\right){x}^{2}+\left(247a^{4}-703a^{3}-792a^{2}+1375a-829\right){x}+3387a^{4}-14884a^{3}-12485a^{2}+30720a-11294$
529.11-a4
529.11-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.11
\( 23^{2} \)
\( - 23^{8} \)
$20.24275$
$(a^2-a-3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$25$
\( 2^{2} \)
$1$
$6.997752932$
1.44581672
\( \frac{675648471455377686001553954708107623}{529} a^{4} + \frac{620911450534242703942927978680242226}{529} a^{3} - \frac{1511073537772727871974027146777724553}{529} a^{2} - \frac{872783469849333360183497166887185757}{529} a + \frac{352086200751501274019816024338865057}{529} \)
\( \bigl[a^{3} - 3 a\) , \( a^{3} - 2 a\) , \( a^{3} - 3 a + 1\) , \( -3637 a^{4} - 5289 a^{3} + 8335 a^{2} + 9042 a - 4717\) , \( 319273 a^{4} + 370615 a^{3} - 699390 a^{2} - 593640 a + 189760\bigr] \)
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(-3637a^{4}-5289a^{3}+8335a^{2}+9042a-4717\right){x}+319273a^{4}+370615a^{3}-699390a^{2}-593640a+189760$
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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.