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
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{18} \)
$10.45765$
$(3a^3+4a^2-17a-13)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Nn
$1$
\( 2 \)
$1$
$66.32247551$
1.694875013
\( -\frac{110592}{125} \)
\( \bigl[0\) , \( 0\) , \( a^{3} + 2 a^{2} - 6 a - 8\) , \( -12 a^{3} - 19 a^{2} + 73 a + 60\) , \( -50 a^{3} - 59 a^{2} + 276 a + 216\bigr] \)
${y}^2+\left(a^{3}+2a^{2}-6a-8\right){y}={x}^{3}+\left(-12a^{3}-19a^{2}+73a+60\right){x}-50a^{3}-59a^{2}+276a+216$
25.1-d1
25.1-d
$1$
$1$
4.4.6125.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{18} \)
$10.45765$
$(3a^3+4a^2-17a-13)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3Nn
$1$
\( 2 \)
$1$
$66.32247551$
1.694875013
\( -\frac{110592}{125} \)
\( \bigl[0\) , \( 0\) , \( a\) , \( 3 a^{3} + 2 a^{2} - 25 a - 19\) , \( 89 a^{3} + 113 a^{2} - 543 a - 431\bigr] \)
${y}^2+a{y}={x}^{3}+\left(3a^{3}+2a^{2}-25a-19\right){x}+89a^{3}+113a^{2}-543a-431$
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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.