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
25.1-a2
25.1-a
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( 5^{8} \)
$23.55381$
$(a^4-2a^3-2a^2+5a)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$884.7644411$
1.15781477
\( \frac{1549868991089}{625} a^{4} - \frac{2463604541892}{625} a^{3} - \frac{5660845609864}{625} a^{2} + \frac{5425940335044}{625} a + \frac{3777390596864}{625} \)
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( 20 a^{4} - 18 a^{3} - 76 a^{2} + 10 a + 20\) , \( 69 a^{4} - 48 a^{3} - 268 a^{2} - 6 a + 54\bigr] \)
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}^{2}+\left(20a^{4}-18a^{3}-76a^{2}+10a+20\right){x}+69a^{4}-48a^{3}-268a^{2}-6a+54$
25.1-d2
25.1-d
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( 5^{8} \)
$23.55381$
$(a^4-2a^3-2a^2+5a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2Cs
$1$
\( 2 \)
$0.400398087$
$1346.796456$
1.76419015
\( \frac{1549868991089}{625} a^{4} - \frac{2463604541892}{625} a^{3} - \frac{5660845609864}{625} a^{2} + \frac{5425940335044}{625} a + \frac{3777390596864}{625} \)
\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( -a^{2} + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 5 a - 1\) , \( -8 a^{4} - 21 a^{3} + 15 a^{2} + 40 a - 7\) , \( -51 a^{4} - 10 a^{3} + 111 a^{2} - a - 9\bigr] \)
${y}^2+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(-8a^{4}-21a^{3}+15a^{2}+40a-7\right){x}-51a^{4}-10a^{3}+111a^{2}-a-9$
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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.