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
28672.6-a2
28672.6-a
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.6
\( 2^{12} \cdot 7 \)
\( 2^{19} \cdot 7^{3} \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.651220208$
$1.946210420$
3.832292328
\( \frac{3358624}{49} a + \frac{16414176}{49} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -26 a + 4\) , \( -64 a + 80\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-26a+4\right){x}-64a+80$
28672.6-f2
28672.6-f
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.6
\( 2^{12} \cdot 7 \)
\( 2^{13} \cdot 7^{3} \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$2.286955994$
$2.752357172$
4.758209668
\( \frac{3358624}{49} a + \frac{16414176}{49} \)
\( \bigl[0\) , \( 1\) , \( 0\) , \( 12 a - 14\) , \( 26 a - 14\bigr] \)
${y}^2={x}^{3}+{x}^{2}+\left(12a-14\right){x}+26a-14$
28672.6-h2
28672.6-h
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.6
\( 2^{12} \cdot 7 \)
\( 2^{19} \cdot 7^{3} \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \cdot 3 \)
$0.503007935$
$1.946210420$
4.440141962
\( \frac{3358624}{49} a + \frac{16414176}{49} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -26 a + 4\) , \( 64 a - 80\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-26a+4\right){x}+64a-80$
28672.6-k2
28672.6-k
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.6
\( 2^{12} \cdot 7 \)
\( 2^{13} \cdot 7^{3} \)
$3.07647$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \cdot 3 \)
$1$
$2.752357172$
3.120879684
\( \frac{3358624}{49} a + \frac{16414176}{49} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a - 14\) , \( -26 a + 14\bigr] \)
${y}^2={x}^{3}-{x}^{2}+\left(12a-14\right){x}-26a+14$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.