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
$1$
$1$
4.4.19225.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{4} \)
$18.52739$
$(a^3-3a^2-7a+15)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.424678925$
$107.5410594$
2.635068041
\( -\frac{947083}{2} a^{3} + \frac{15795853}{10} a^{2} + \frac{34133251}{10} a - \frac{44592797}{5} \)
\( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{5}{2} a + 9\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{7}{2} a - 14\) , \( -a^{3} + 4 a^{2} + 6 a - 23\) , \( -a^{3} + 11 a^{2} + 13 a - 48\) , \( \frac{5}{2} a^{3} + \frac{21}{2} a^{2} - \frac{13}{2} a - 45\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{5}{2}a+9\right){x}{y}+\left(-a^{3}+4a^{2}+6a-23\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{7}{2}a-14\right){x}^{2}+\left(-a^{3}+11a^{2}+13a-48\right){x}+\frac{5}{2}a^{3}+\frac{21}{2}a^{2}-\frac{13}{2}a-45$
25.1-b1
25.1-b
$1$
$1$
4.4.19225.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{4} \)
$18.52739$
$(a^3-3a^2-7a+15)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.424678925$
$107.5410594$
2.635068041
\( -\frac{134361}{5} a^{3} - \frac{391721}{5} a^{2} + \frac{447854}{5} a + \frac{1473199}{5} \)
\( \bigl[-\frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{5}{2} a - 15\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a^{2} - \frac{7}{2} a + 14\) , \( -a^{3} + 4 a^{2} + 7 a - 23\) , \( -\frac{13}{2} a^{3} + \frac{43}{2} a^{2} + \frac{85}{2} a - 101\) , \( -11 a^{3} + 36 a^{2} + 71 a - 176\bigr] \)
${y}^2+\left(-\frac{1}{2}a^{3}+\frac{5}{2}a^{2}+\frac{5}{2}a-15\right){x}{y}+\left(-a^{3}+4a^{2}+7a-23\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a^{2}-\frac{7}{2}a+14\right){x}^{2}+\left(-\frac{13}{2}a^{3}+\frac{43}{2}a^{2}+\frac{85}{2}a-101\right){x}-11a^{3}+36a^{2}+71a-176$
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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.