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
1764.2-a1
1764.2-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1764.2
\( 2^{2} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{2} \cdot 7^{4} \)
$1.63798$
$(a), (-a-1), (a-1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$0.724148694$
$3.823324891$
1.957735241
\( -\frac{16384}{147} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( -2\bigr] \)
${y}^2={x}^{3}-{x}^{2}-{x}-2$
7056.2-d1
7056.2-d
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
7056.2
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{2} \cdot 7^{4} \)
$2.31645$
$(a), (-a-1), (a-1), (7)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$3.823324891$
2.703498957
\( -\frac{16384}{147} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 2\bigr] \)
${y}^2={x}^{3}+{x}^{2}-{x}+2$
15876.3-a1
15876.3-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
15876.3
\( 2^{2} \cdot 3^{4} \cdot 7^{2} \)
\( 2^{8} \cdot 3^{14} \cdot 7^{4} \)
$2.83706$
$(a), (-a-1), (a-1), (7)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{5} \cdot 3 \)
$0.097774690$
$1.274441630$
4.229340360
\( -\frac{16384}{147} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( 65\bigr] \)
${y}^2={x}^{3}-12{x}+65$
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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.