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
784.3-CMb1
784.3-CMb
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
784.3
\( 2^{4} \cdot 7^{2} \)
\( 2^{16} \cdot 7^{10} \)
$0.81899$
$(3a-2), (2)$
0
$\mathsf{trivial}$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$7$
7Cs.2.1
$1$
\( 1 \)
$1$
$1.101251020$
1.271615146
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( -94 a - 11\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-94a-11$
784.3-CMa1
784.3-CMa
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
784.3
\( 2^{4} \cdot 7^{2} \)
\( 2^{8} \cdot 7^{6} \)
$0.81899$
$(3a-2), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$2, 7$
2Cs , 7Cs.2.1
$1$
\( 2^{2} \)
$1$
$3.344046705$
0.965343132
\( 0 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 2 a + 2\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}+2a+2$
784.3-CMa2
784.3-CMa
$2$
$2$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
784.3
\( 2^{4} \cdot 7^{2} \)
\( 2^{16} \cdot 7^{6} \)
$0.81899$
$(3a-2), (2)$
0
$\Z/2\Z$
$\textsf{yes}$
$-12$
$\mathrm{U}(1)$
✓
✓
$7$
7Cs.2.1
$1$
\( 2 \)
$1$
$1.672023352$
0.965343132
\( 54000 \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -14 a - 25\) , \( 67 a + 45\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a-25\right){x}+67a+45$
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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.