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-a1
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
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$1$
$1769.528882$
1.15781477
\( \frac{708112}{25} a^{4} - \frac{1125079}{25} a^{3} - \frac{2581192}{25} a^{2} + \frac{496376}{5} a + \frac{1711623}{25} \)
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 5\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( 2 a^{4} - 2 a^{3} - 4 a^{2} + 4 a\) , \( 2 a^{4} - a^{3} - 5 a^{2} + 2 a\bigr] \)
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+8a^{2}-7a-5\right){x}^{2}+\left(2a^{4}-2a^{3}-4a^{2}+4a\right){x}+2a^{4}-a^{3}-5a^{2}+2a$
25.1-d1
25.1-d
$4$
$4$
5.5.36497.1
$5$
$[5, 0]$
25.1
\( 5^{2} \)
\( 5^{4} \)
$23.55381$
$(a^4-2a^3-2a^2+5a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.200199043$
$2693.592912$
1.76419015
\( \frac{708112}{25} a^{4} - \frac{1125079}{25} a^{3} - \frac{2581192}{25} a^{2} + \frac{496376}{5} a + \frac{1711623}{25} \)
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{2} - 1\) , \( 3 a^{4} - 6 a^{3} - 10 a^{2} + 13 a + 6\) , \( -20 a^{4} + 12 a^{3} + 77 a^{2} + 9 a - 11\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+3\right){x}^{2}+\left(3a^{4}-6a^{3}-10a^{2}+13a+6\right){x}-20a^{4}+12a^{3}+77a^{2}+9a-11$
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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.