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
1936.8-a1
1936.8-a
$2$
$3$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
1936.8
\( 2^{4} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{6} \)
$1.56825$
$(a), (-a+1), (-2a+3), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$1.303707704$
$1.228722931$
2.421838433
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \)
${y}^2={x}^{3}+{x}^{2}-77{x}-289$
30976.14-a1
30976.14-a
$2$
$3$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
30976.14
\( 2^{8} \cdot 11^{2} \)
\( 2^{16} \cdot 11^{6} \)
$3.13649$
$(a), (-a+1), (-2a+3), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B
$1$
\( 2^{2} \cdot 3^{2} \)
$0.058354610$
$1.228722931$
3.902497262
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( -77\) , \( 289\bigr] \)
${y}^2={x}^{3}-{x}^{2}-77{x}+289$
30976.20-a1
30976.20-a
$2$
$3$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
30976.20
\( 2^{8} \cdot 11^{2} \)
\( 2^{22} \cdot 11^{6} \)
$3.13649$
$(a), (-a+1), (-2a+3), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 3^{2} \)
$0.418504952$
$0.868838317$
4.947582537
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 77 a + 77\) , \( 289 a - 867\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(77a+77\right){x}+289a-867$
30976.8-a1
30976.8-a
$2$
$3$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
30976.8
\( 2^{8} \cdot 11^{2} \)
\( 2^{22} \cdot 11^{6} \)
$3.13649$
$(a), (-a+1), (-2a+3), (2a+1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B
$1$
\( 3^{2} \)
$0.418504952$
$0.868838317$
4.947582537
\( -\frac{199794688}{1331} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -77 a + 154\) , \( -289 a - 578\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-77a+154\right){x}-289a-578$
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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.