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
5.1-a4
5.1-a
$6$
$8$
4.4.13025.1
$4$
$[4, 0]$
5.1
\( 5 \)
\( 5^{2} \)
$12.47093$
$(1/4a^3+1/2a^2-1/2a-7/4)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2 \)
$0.279001129$
$1484.251472$
1.814239378
\( -\frac{5243081}{20} a^{3} - \frac{2114437}{10} a^{2} + \frac{27643383}{10} a + \frac{84189419}{20} \)
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a + \frac{9}{4}\) , \( -a - 1\) , \( a^{2} - 5\) , \( -\frac{7}{2} a^{3} + a^{2} + 12 a - \frac{5}{2}\) , \( \frac{39}{4} a^{3} + \frac{27}{2} a^{2} - \frac{65}{2} a - \frac{177}{4}\bigr] \)
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{3}{2}a+\frac{9}{4}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-\frac{7}{2}a^{3}+a^{2}+12a-\frac{5}{2}\right){x}+\frac{39}{4}a^{3}+\frac{27}{2}a^{2}-\frac{65}{2}a-\frac{177}{4}$
25.3-a6
25.3-a
$6$
$8$
4.4.13025.1
$4$
$[4, 0]$
25.3
\( 5^{2} \)
\( 5^{8} \)
$15.25000$
$(1/4a^3+1/2a^2-1/2a-7/4)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2 \)
$1$
$224.2136840$
3.929191938
\( -\frac{5243081}{20} a^{3} - \frac{2114437}{10} a^{2} + \frac{27643383}{10} a + \frac{84189419}{20} \)
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a + \frac{9}{4}\) , \( \frac{1}{4} a^{3} - \frac{3}{2} a^{2} + \frac{1}{2} a + \frac{25}{4}\) , \( -\frac{1}{4} a^{3} + \frac{3}{2} a^{2} + \frac{1}{2} a - \frac{29}{4}\) , \( \frac{493}{2} a^{3} - 709 a^{2} - 1618 a + \frac{7551}{2}\) , \( -\frac{14395}{4} a^{3} + \frac{20799}{2} a^{2} + \frac{47125}{2} a - \frac{221387}{4}\bigr] \)
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{2}a^{2}-\frac{1}{2}a+\frac{9}{4}\right){x}{y}+\left(-\frac{1}{4}a^{3}+\frac{3}{2}a^{2}+\frac{1}{2}a-\frac{29}{4}\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{3}{2}a^{2}+\frac{1}{2}a+\frac{25}{4}\right){x}^{2}+\left(\frac{493}{2}a^{3}-709a^{2}-1618a+\frac{7551}{2}\right){x}-\frac{14395}{4}a^{3}+\frac{20799}{2}a^{2}+\frac{47125}{2}a-\frac{221387}{4}$
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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.