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
20.2-b2
20.2-b
$2$
$3$
4.4.12400.1
$4$
$[4, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( - 2^{6} \cdot 5 \)
$14.47032$
$(-1/2a^3-3/2a^2+3/2a+11/2), (-a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$0.116055896$
$778.1746306$
3.244093983
\( \frac{2135237909}{40} a^{3} - \frac{4142533731}{40} a^{2} - \frac{17585965949}{40} a + \frac{34118238951}{40} \)
\( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{31}{2} a^{3} + \frac{87}{2} a^{2} - \frac{117}{2} a - \frac{327}{2}\) , \( -22 a^{3} - 64 a^{2} + 83 a + 241\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{5}{2}a+1\right){y}={x}^{3}+\left(\frac{1}{2}a^{3}-\frac{1}{2}a^{2}-\frac{5}{2}a+\frac{5}{2}\right){x}^{2}+\left(\frac{31}{2}a^{3}+\frac{87}{2}a^{2}-\frac{117}{2}a-\frac{327}{2}\right){x}-22a^{3}-64a^{2}+83a+241$
20.2-c2
20.2-c
$2$
$3$
4.4.12400.1
$4$
$[4, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( - 2^{6} \cdot 5 \)
$14.47032$
$(-1/2a^3-3/2a^2+3/2a+11/2), (-a+3)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 1 \)
$1$
$129.2017712$
1.160266157
\( \frac{2135237909}{40} a^{3} - \frac{4142533731}{40} a^{2} - \frac{17585965949}{40} a + \frac{34118238951}{40} \)
\( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a + 1\) , \( \frac{13}{2} a^{3} + 18 a^{2} - \frac{49}{2} a - 66\) , \( a^{3} + 4 a^{2} - 3 a - 18\bigr] \)
${y}^2+\left(\frac{1}{2}a^{3}+\frac{1}{2}a^{2}-\frac{5}{2}a-\frac{7}{2}\right){x}{y}+\left(\frac{1}{2}a^{3}-\frac{7}{2}a+1\right){y}={x}^{3}+a{x}^{2}+\left(\frac{13}{2}a^{3}+18a^{2}-\frac{49}{2}a-66\right){x}+a^{3}+4a^{2}-3a-18$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.