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-a4
25.1-a
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( 5^{4} \)
$23.55381$
$(a^4-2a^3-2a^2+5a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$442.3822205$
1.15781477
\( \frac{488509962822731359638}{25} a^{4} - \frac{776547463172625188346}{25} a^{3} - \frac{1784205847864588683433}{25} a^{2} + \frac{342071130235394451034}{5} a + \frac{1190397818850374480652}{25} \)
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a - 2\) , \( a^{2} - 1\) , \( -53 a^{4} + 93 a^{3} + 155 a^{2} - 135 a - 149\) , \( -157 a^{4} + 112 a^{3} + 991 a^{2} - 666 a - 644\bigr] \)
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-4a-2\right){x}^{2}+\left(-53a^{4}+93a^{3}+155a^{2}-135a-149\right){x}-157a^{4}+112a^{3}+991a^{2}-666a-644$
25.1-d4
25.1-d
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( 5^{4} \)
$23.55381$
$(a^4-2a^3-2a^2+5a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2 \)
$0.800796175$
$42.08738925$
1.76419015
\( \frac{488509962822731359638}{25} a^{4} - \frac{776547463172625188346}{25} a^{3} - \frac{1784205847864588683433}{25} a^{2} + \frac{342071130235394451034}{5} a + \frac{1190397818850374480652}{25} \)
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{2} - 1\) , \( 143 a^{4} - 101 a^{3} - 555 a^{2} + 8 a + 86\) , \( 747 a^{4} - 457 a^{3} - 2953 a^{2} - 247 a + 559\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+3\right){x}^{2}+\left(143a^{4}-101a^{3}-555a^{2}+8a+86\right){x}+747a^{4}-457a^{3}-2953a^{2}-247a+559$
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Pari/GP
SageMath
Magma
Oscar
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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.