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
224.6-a1
224.6-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.6
\( 2^{5} \cdot 7 \)
\( 2^{9} \cdot 7 \)
$0.91464$
$(-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 1 \)
$1$
$6.944288598$
1.312347190
\( \frac{2525}{7} a + \frac{8121}{7} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+{x}$
224.6-a2
224.6-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.6
\( 2^{5} \cdot 7 \)
\( 2^{6} \cdot 7^{2} \)
$0.91464$
$(-a+1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$6.944288598$
1.312347190
\( -\frac{3555}{7} a + \frac{15857}{7} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -2\) , \( -a - 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-2{x}-a-1$
224.6-a3
224.6-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.6
\( 2^{5} \cdot 7 \)
\( 2^{9} \cdot 7^{4} \)
$0.91464$
$(-a+1), (-2a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.472144299$
1.312347190
\( \frac{1482409}{49} a + \frac{907013}{49} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 5 a - 7\) , \( 5 a - 7\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(5a-7\right){x}+5a-7$
224.6-a4
224.6-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.6
\( 2^{5} \cdot 7 \)
\( 2^{12} \cdot 7 \)
$0.91464$
$(-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$3.472144299$
1.312347190
\( -\frac{9225207}{7} a + \frac{9710861}{7} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 10 a - 7\) , \( -10 a - 21\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(10a-7\right){x}-10a-21$
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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.