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
784.1-c1
784.1-c
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{4} \)
$2.16684$
$(a+3), (2)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B.1.1
$1$
\( 3^{2} \)
$1$
$17.19445586$
3.752137883
\( 1792 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 31\) , \( 13 a - 37\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(12a-31\right){x}+13a-37$
784.1-d1
784.1-d
$2$
$3$
\(\Q(\sqrt{21}) \)
$2$
$[2, 0]$
784.1
\( 2^{4} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{4} \)
$2.16684$
$(a+3), (2)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2Cn , 3B.1.2
$1$
\( 3^{2} \)
$0.019390460$
$19.01761041$
2.896922752
\( 1792 \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 1\bigr] \)
${y}^2={x}^{3}-{x}^{2}-2{x}+1$
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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.