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
20.1-a1
20.1-a
$2$
$2$
4.4.18625.1
$4$
$[4, 0]$
20.1
\( 2^{2} \cdot 5 \)
\( 2^{4} \cdot 5^{4} \)
$17.73436$
$(1/2a^3+a^2-5a-21/2), (-a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{2} \)
$0.445305190$
$359.4527298$
4.691496469
\( -\frac{214001}{60} a^{3} + \frac{305383}{20} a^{2} + \frac{54853}{60} a - \frac{124942}{3} \)
\( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a + \frac{1}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{7}{6} a^{3} - a^{2} + \frac{31}{3} a + \frac{71}{6}\) , \( \frac{413}{6} a^{3} + 103 a^{2} - \frac{2147}{3} a - \frac{6973}{6}\bigr] \)
${y}^2+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{1}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{3}a+\frac{1}{6}\right){x}^{2}+\left(-\frac{7}{6}a^{3}-a^{2}+\frac{31}{3}a+\frac{71}{6}\right){x}+\frac{413}{6}a^{3}+103a^{2}-\frac{2147}{3}a-\frac{6973}{6}$
20.1-d1
20.1-d
$2$
$2$
4.4.18625.1
$4$
$[4, 0]$
20.1
\( 2^{2} \cdot 5 \)
\( 2^{4} \cdot 5^{4} \)
$17.73436$
$(1/2a^3+a^2-5a-21/2), (-a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$1$
\( 2^{3} \)
$0.045563058$
$923.3538492$
2.466169251
\( -\frac{214001}{60} a^{3} + \frac{305383}{20} a^{2} + \frac{54853}{60} a - \frac{124942}{3} \)
\( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{1}{3} a - \frac{41}{6}\) , \( -\frac{1}{6} a^{3} - a^{2} + \frac{1}{3} a + \frac{35}{6}\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( \frac{3}{2} a^{3} - a^{2} - 10 a + \frac{19}{2}\) , \( \frac{5}{6} a^{3} + 3 a^{2} - \frac{23}{3} a - \frac{73}{6}\bigr] \)
${y}^2+\left(\frac{1}{6}a^{3}+a^{2}-\frac{1}{3}a-\frac{41}{6}\right){x}{y}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{6}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-a^{2}+\frac{1}{3}a+\frac{35}{6}\right){x}^{2}+\left(\frac{3}{2}a^{3}-a^{2}-10a+\frac{19}{2}\right){x}+\frac{5}{6}a^{3}+3a^{2}-\frac{23}{3}a-\frac{73}{6}$
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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.