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
16641.2-a1
16641.2-a
$1$
$1$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
16641.2
\( 3^{2} \cdot 43^{2} \)
\( 3^{8} \cdot 43^{2} \)
$2.68524$
$(-2a+7), (2a+5), (3)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 2^{2} \)
$0.123910393$
$2.545244737$
3.814505486
\( -\frac{799178752}{3483} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -19\) , \( 39\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-19{x}+39$
16641.2-b1
16641.2-b
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
16641.2
\( 3^{2} \cdot 43^{2} \)
\( 3^{6} \cdot 43^{8} \)
$2.68524$
$(-2a+7), (2a+5), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$1$
$0.648136583$
1.469835612
\( \frac{129784785047}{92307627} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 105\) , \( -191\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+105{x}-191$
16641.2-b2
16641.2-b
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
16641.2
\( 3^{2} \cdot 43^{2} \)
\( 3^{12} \cdot 43^{4} \)
$2.68524$
$(-2a+7), (2a+5), (3)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{3} \cdot 3 \)
$1$
$1.296273166$
1.469835612
\( \frac{2845178713}{1347921} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -30\) , \( -29\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-30{x}-29$
16641.2-b3
16641.2-b
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
16641.2
\( 3^{2} \cdot 43^{2} \)
\( 3^{24} \cdot 43^{2} \)
$2.68524$
$(-2a+7), (2a+5), (3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 2^{2} \cdot 3 \)
$1$
$0.648136583$
1.469835612
\( \frac{1616855892553}{22851963} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -245\) , \( 1433\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-245{x}+1433$
16641.2-b4
16641.2-b
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
16641.2
\( 3^{2} \cdot 43^{2} \)
\( 3^{6} \cdot 43^{2} \)
$2.68524$
$(-2a+7), (2a+5), (3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 3 \)
$1$
$2.592546333$
1.469835612
\( \frac{1630532233}{1161} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -25\) , \( -49\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-25{x}-49$
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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.