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
14336.9-b1
14336.9-b
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
14336.9
\( 2^{11} \cdot 7 \)
\( 2^{17} \cdot 7 \)
$2.58699$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$0.299194391$
$4.423751828$
4.002074513
\( -\frac{1072}{7} a + \frac{3280}{7} \)
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+2a{x}$
14336.9-c1
14336.9-c
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
14336.9
\( 2^{11} \cdot 7 \)
\( 2^{23} \cdot 7 \)
$2.58699$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.741219377$
$3.128064916$
3.505366995
\( -\frac{1072}{7} a + \frac{3280}{7} \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2 a + 1\) , \( 3 a - 2\bigr] \)
${y}^2={x}^{3}-a{x}^{2}+\left(-2a+1\right){x}+3a-2$
28672.9-c1
28672.9-c
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.9
\( 2^{12} \cdot 7 \)
\( 2^{23} \cdot 7 \)
$3.07647$
$(a), (-a+1), (-2a+1)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$0.949735186$
$3.128064916$
4.491477793
\( -\frac{1072}{7} a + \frac{3280}{7} \)
\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a + 1\) , \( -3 a + 2\bigr] \)
${y}^2={x}^{3}+a{x}^{2}+\left(-2a+1\right){x}-3a+2$
28672.9-n1
28672.9-n
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
28672.9
\( 2^{12} \cdot 7 \)
\( 2^{17} \cdot 7 \)
$3.07647$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.423751828$
3.344042057
\( -\frac{1072}{7} a + \frac{3280}{7} \)
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+2a{x}$
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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.