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-d3
20.1-d
$4$
$4$
4.4.10025.1
$4$
$[4, 0]$
20.1
\( 2^{2} \cdot 5 \)
\( 2^{2} \cdot 5 \)
$13.01096$
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$4$
\( 1 \)
$1$
$120.9106636$
1.207598081
\( \frac{108228121969295379}{20} a^{3} + \frac{179433515162009521}{20} a^{2} - \frac{713589500604580069}{20} a - \frac{81438223753542063}{2} \)
\( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + \frac{9}{2} a + 4\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( -17 a^{3} - 29 a^{2} + 113 a + 125\) , \( -\frac{393}{2} a^{3} - \frac{653}{2} a^{2} + \frac{2563}{2} a + 1462\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){x}{y}+\left(\frac{1}{2}a^{3}+\frac{3}{2}a^{2}-\frac{5}{2}a-7\right){y}={x}^{3}+\left(-\frac{1}{2}a^{3}-\frac{1}{2}a^{2}+\frac{9}{2}a+4\right){x}^{2}+\left(-17a^{3}-29a^{2}+113a+125\right){x}-\frac{393}{2}a^{3}-\frac{653}{2}a^{2}+\frac{2563}{2}a+1462$
100.1-j3
100.1-j
$4$
$4$
4.4.10025.1
$4$
$[4, 0]$
100.1
\( 2^{2} \cdot 5^{2} \)
\( 2^{2} \cdot 5^{7} \)
$15.91039$
$(-a^3-a^2+8a+5), (-2a^3-3a^2+13a+14)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1.005937518$
$19.54971462$
3.142600828
\( \frac{108228121969295379}{20} a^{3} + \frac{179433515162009521}{20} a^{2} - \frac{713589500604580069}{20} a - \frac{81438223753542063}{2} \)
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - 3\) , \( -a^{3} - 2 a^{2} + 6 a + 12\) , \( a^{3} + 2 a^{2} - 6 a - 11\) , \( \frac{143}{2} a^{3} + \frac{197}{2} a^{2} - \frac{1099}{2} a - 596\) , \( 587 a^{3} + 821 a^{2} - 4488 a - 4913\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{7}{2}a-3\right){x}{y}+\left(a^{3}+2a^{2}-6a-11\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+6a+12\right){x}^{2}+\left(\frac{143}{2}a^{3}+\frac{197}{2}a^{2}-\frac{1099}{2}a-596\right){x}+587a^{3}+821a^{2}-4488a-4913$
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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.