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-c2
28672.6-c
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.6
\( 2^{12} \cdot 7 \)
\( 2^{14} \cdot 7 \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$2$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.464355675$
$4.525264338$
6.353831277
\( \frac{60864}{7} a + \frac{88064}{7} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 1\) , \( -3 a + 5\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+1\right){x}-3a+5$
28672.6-d2
28672.6-d
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.6
\( 2^{12} \cdot 7 \)
\( 2^{20} \cdot 7 \)
$3.07647$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$3.199845100$
2.418855533
\( \frac{60864}{7} a + \frac{88064}{7} \)
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a + 3\) , \( a - 5\bigr] \)
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a+3\right){x}+a-5$
28672.6-i2
28672.6-i
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.6
\( 2^{12} \cdot 7 \)
\( 2^{14} \cdot 7 \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.754812959$
$4.525264338$
5.164095586
\( \frac{60864}{7} a + \frac{88064}{7} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 1\) , \( 3 a - 5\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+1\right){x}+3a-5$
28672.6-j2
28672.6-j
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.6
\( 2^{12} \cdot 7 \)
\( 2^{20} \cdot 7 \)
$3.07647$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$3.199845100$
2.418855533
\( \frac{60864}{7} a + \frac{88064}{7} \)
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a + 3\) , \( -a + 5\bigr] \)
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+3\right){x}-a+5$
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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.