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-a1
20.2-a
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{18} \cdot 5 \)
$1.01764$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.2
$1$
\( 3^{2} \)
$1$
$0.902214666$
1.507833519
\( -\frac{19984640951}{640} a - \frac{175841574349}{2560} \)
\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 142 a - 449\) , \( 1521 a - 4857\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(142a-449\right){x}+1521a-4857$
20.2-a2
20.2-a
$2$
$3$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{6} \cdot 5^{3} \)
$1.01764$
$(-a+2), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1
$1$
\( 3^{2} \)
$1$
$8.119932001$
1.507833519
\( -\frac{124021}{1000} a + \frac{296769}{1000} \)
\( \bigl[1\) , \( a\) , \( a\) , \( -2 a - 2\) , \( -13 a - 30\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2a-2\right){x}-13a-30$
20.2-b1
20.2-b
$1$
$1$
\(\Q(\sqrt{29}) \)
$2$
$[2, 0]$
20.2
\( 2^{2} \cdot 5 \)
\( 2^{2} \cdot 5^{7} \)
$1.01764$
$(-a+2), (2)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$1$
$5.994874057$
1.113220165
\( \frac{119629571}{156250} a - \frac{118018719}{156250} \)
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( a + 1\) , \( a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(a+1\right){x}+a+1$
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.