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-c2
25.1-c
$6$
$8$
4.4.9225.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{16} \)
$12.83407$
$(1/2a^3-3a-1/2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$0.094469396$
$290.8077153$
2.288252076
\( -\frac{10463690358987}{2500} a^{3} + \frac{9678146215168}{625} a^{2} + \frac{12827568843}{250} a - \frac{14724711948631}{500} \)
\( \bigl[\frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{19}{4}\) , \( -\frac{1}{4} a^{3} - a^{2} + \frac{5}{2} a + \frac{15}{4}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a + \frac{1}{4}\) , \( -\frac{687}{4} a^{3} - 292 a^{2} + \frac{1835}{2} a + \frac{4905}{4}\) , \( \frac{9607}{4} a^{3} + 4492 a^{2} - \frac{22469}{2} a - \frac{63205}{4}\bigr] \)
${y}^2+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{19}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a+\frac{1}{4}\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-a^{2}+\frac{5}{2}a+\frac{15}{4}\right){x}^{2}+\left(-\frac{687}{4}a^{3}-292a^{2}+\frac{1835}{2}a+\frac{4905}{4}\right){x}+\frac{9607}{4}a^{3}+4492a^{2}-\frac{22469}{2}a-\frac{63205}{4}$
25.1-d5
25.1-d
$6$
$8$
4.4.9225.1
$4$
$[4, 0]$
25.1
\( 5^{2} \)
\( 5^{16} \)
$12.83407$
$(1/2a^3-3a-1/2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 2^{3} \)
$1.469838141$
$5.175558822$
2.534507336
\( -\frac{10463690358987}{2500} a^{3} + \frac{9678146215168}{625} a^{2} + \frac{12827568843}{250} a - \frac{14724711948631}{500} \)
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a + \frac{1}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( \frac{1}{4} a^{3} + a^{2} - \frac{3}{2} a - \frac{15}{4}\) , \( -\frac{241}{4} a^{3} - 53 a^{2} + \frac{915}{2} a + \frac{1799}{4}\) , \( \frac{707}{2} a^{3} + 404 a^{2} - 2799 a - \frac{7087}{2}\bigr] \)
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a+\frac{1}{4}\right){x}{y}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+a^{2}-\frac{3}{2}a-\frac{15}{4}\right){x}^{2}+\left(-\frac{241}{4}a^{3}-53a^{2}+\frac{915}{2}a+\frac{1799}{4}\right){x}+\frac{707}{2}a^{3}+404a^{2}-2799a-\frac{7087}{2}$
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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.