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
23.2-a2
23.2-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.2
\( 23 \)
\( - 23^{10} \)
$14.79438$
$(-a^4+3a^2+a-2)$
0
$\Z/10\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.1
$1$
\( 2 \cdot 5 \)
$1$
$993.1260669$
0.820765345
\( -\frac{47416580387872896214}{41426511213649} a^{4} + \frac{88354860075954926274}{41426511213649} a^{3} + \frac{114797344933419666883}{41426511213649} a^{2} - \frac{244287782065752925838}{41426511213649} a + \frac{64820146352754535654}{41426511213649} \)
\( \bigl[a^{4} + a^{3} - 3 a^{2} - 2 a + 1\) , \( a^{2} + a - 1\) , \( a^{4} + a^{3} - 4 a^{2} - 2 a + 2\) , \( 49 a^{4} - 67 a^{3} - 121 a^{2} + 192 a - 44\) , \( 233 a^{4} - 388 a^{3} - 573 a^{2} + 1088 a - 256\bigr] \)
${y}^2+\left(a^{4}+a^{3}-3a^{2}-2a+1\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-2a+2\right){y}={x}^{3}+\left(a^{2}+a-1\right){x}^{2}+\left(49a^{4}-67a^{3}-121a^{2}+192a-44\right){x}+233a^{4}-388a^{3}-573a^{2}+1088a-256$
529.14-a2
529.14-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.14
\( 23^{2} \)
\( - 23^{16} \)
$20.24275$
$(-a^4+3a^2+a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.1
$1$
\( 2^{2} \)
$1$
$174.9438233$
1.44581672
\( -\frac{47416580387872896214}{41426511213649} a^{4} + \frac{88354860075954926274}{41426511213649} a^{3} + \frac{114797344933419666883}{41426511213649} a^{2} - \frac{244287782065752925838}{41426511213649} a + \frac{64820146352754535654}{41426511213649} \)
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 1\) , \( -17 a^{4} - 3 a^{3} + 94 a^{2} + 8 a - 117\) , \( -157 a^{4} + 133 a^{3} + 635 a^{2} - 364 a - 450\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-17a^{4}-3a^{3}+94a^{2}+8a-117\right){x}-157a^{4}+133a^{3}+635a^{2}-364a-450$
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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.