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-a4
23.1-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
23.1
\( 23 \)
\( - 23^{2} \)
$14.79438$
$(a^4-3a^2-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 5$
2B , 5B.1.2
$625$
\( 2 \)
$1$
$0.317800341$
0.820765345
\( \frac{1812431798583025575975116650734948165}{529} a^{4} - \frac{1296559921989620389944481933388349849}{529} a^{3} - \frac{7618766625551254351602825393413091355}{529} a^{2} + \frac{3268768315434618465890517821484807321}{529} a + \frac{6367683864076909597378964320128797635}{529} \)
\( \bigl[a^{4} - 3 a^{2} + a + 1\) , \( a^{4} + a^{3} - 4 a^{2} - 4 a + 2\) , \( a^{4} - 3 a^{2} + 1\) , \( -959 a^{4} - 683 a^{3} + 2238 a^{2} + 491 a - 1224\) , \( -40616 a^{4} - 34613 a^{3} + 92332 a^{2} + 42697 a - 29653\bigr] \)
${y}^2+\left(a^{4}-3a^{2}+a+1\right){x}{y}+\left(a^{4}-3a^{2}+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-4a^{2}-4a+2\right){x}^{2}+\left(-959a^{4}-683a^{3}+2238a^{2}+491a-1224\right){x}-40616a^{4}-34613a^{3}+92332a^{2}+42697a-29653$
529.12-a4
529.12-a
$4$
$10$
\(\Q(\zeta_{11})^+\)
$5$
$[5, 0]$
529.12
\( 23^{2} \)
\( - 23^{8} \)
$20.24275$
$(a^4-3a^2-1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 5$
2B , 5B.4.2
$25$
\( 2^{2} \)
$1$
$6.997752932$
1.44581672
\( \frac{1812431798583025575975116650734948165}{529} a^{4} - \frac{1296559921989620389944481933388349849}{529} a^{3} - \frac{7618766625551254351602825393413091355}{529} a^{2} + \frac{3268768315434618465890517821484807321}{529} a + \frac{6367683864076909597378964320128797635}{529} \)
\( \bigl[1\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a - 2\) , \( a^{2} + a - 1\) , \( -7642 a^{4} - 981 a^{3} + 23763 a^{2} - 2800 a - 15793\) , \( 572002 a^{4} + 201731 a^{3} - 1679848 a^{2} - 156291 a + 872066\bigr] \)
${y}^2+{x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-3a-2\right){x}^{2}+\left(-7642a^{4}-981a^{3}+23763a^{2}-2800a-15793\right){x}+572002a^{4}+201731a^{3}-1679848a^{2}-156291a+872066$
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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.