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
25.2-a1
25.2-a
$1$
$1$
6.6.1241125.1
$6$
$[6, 0]$
25.2
\( 5^{2} \)
\( 5^{3} \)
$130.17912$
$(-2a^5+a^4+13a^3-2a^2-19a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.008964453$
$31253.00479$
3.01779
\( -2708 a^{5} + 733 a^{4} + 12894 a^{3} - 3948 a^{2} - 9886 a - 1842 \)
\( \bigl[-a^{5} + 7 a^{3} + 2 a^{2} - 10 a - 6\) , \( 2 a^{5} - a^{4} - 13 a^{3} + 2 a^{2} + 20 a + 5\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 53 a - 19\) , \( -6 a^{5} + 2 a^{4} + 40 a^{3} - 60 a - 21\) , \( -5 a^{5} + a^{4} + 35 a^{3} + 3 a^{2} - 55 a - 24\bigr] \)
${y}^2+\left(-a^{5}+7a^{3}+2a^{2}-10a-6\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-53a-19\right){y}={x}^{3}+\left(2a^{5}-a^{4}-13a^{3}+2a^{2}+20a+5\right){x}^{2}+\left(-6a^{5}+2a^{4}+40a^{3}-60a-21\right){x}-5a^{5}+a^{4}+35a^{3}+3a^{2}-55a-24$
25.2-d1
25.2-d
$1$
$1$
6.6.1241125.1
$6$
$[6, 0]$
25.2
\( 5^{2} \)
\( 5^{9} \)
$130.17912$
$(-2a^5+a^4+13a^3-2a^2-19a-5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.020207192$
$12955.98893$
2.82001
\( -2708 a^{5} + 733 a^{4} + 12894 a^{3} - 3948 a^{2} - 9886 a - 1842 \)
\( \bigl[a^{2} + a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( -8 a^{5} + 3 a^{4} + 53 a^{3} - 5 a^{2} - 79 a - 22\) , \( -8 a^{5} + 3 a^{4} + 54 a^{3} - 4 a^{2} - 83 a - 27\bigr] \)
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(-5a^{5}+2a^{4}+34a^{3}-2a^{2}-52a-19\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}^{2}+\left(-8a^{5}+3a^{4}+53a^{3}-5a^{2}-79a-22\right){x}-8a^{5}+3a^{4}+54a^{3}-4a^{2}-83a-27$
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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.