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-a3
25.1-a
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( - 5^{16} \)
$23.55381$
$(a^4-2a^3-2a^2+5a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2^{3} \)
$1$
$27.64888878$
1.15781477
\( -\frac{136402392772743238}{390625} a^{4} + \frac{341339187700279242}{390625} a^{3} + \frac{236740655090238193}{390625} a^{2} - \frac{799831738588792786}{390625} a + \frac{268640638721913956}{390625} \)
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -5 a^{4} - 14 a^{3} - 11 a^{2} + 55 a - 20\) , \( -63 a^{4} - 115 a^{3} + 166 a^{2} + 193 a - 100\bigr] \)
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-4\right){x}^{2}+\left(-5a^{4}-14a^{3}-11a^{2}+55a-20\right){x}-63a^{4}-115a^{3}+166a^{2}+193a-100$
25.1-d3
25.1-d
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( - 5^{16} \)
$23.55381$
$(a^4-2a^3-2a^2+5a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.200199043$
$673.3982280$
1.76419015
\( -\frac{136402392772743238}{390625} a^{4} + \frac{341339187700279242}{390625} a^{3} + \frac{236740655090238193}{390625} a^{2} - \frac{799831738588792786}{390625} a + \frac{268640638721913956}{390625} \)
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 1\) , \( a^{2} - 2\) , \( 89 a^{4} - 17 a^{3} - 439 a^{2} - 38 a + 86\) , \( -819 a^{4} + 586 a^{3} + 3095 a^{2} + 134 a - 596\bigr] \)
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a+1\right){x}^{2}+\left(89a^{4}-17a^{3}-439a^{2}-38a+86\right){x}-819a^{4}+586a^{3}+3095a^{2}+134a-596$
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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.