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
224.1-a1
224.1-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.1
\( 2^{5} \cdot 7 \)
\( 2^{9} \cdot 7 \)
$0.91464$
$(a), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 1 \)
$1$
$6.944288598$
1.312347190
\( -\frac{2525}{7} a + \frac{10646}{7} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+{x}$
224.1-a2
224.1-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.1
\( 2^{5} \cdot 7 \)
\( 2^{6} \cdot 7^{2} \)
$0.91464$
$(a), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{2} \)
$1$
$6.944288598$
1.312347190
\( \frac{3555}{7} a + \frac{12302}{7} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -2 a + 1\) , \( 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+1\right){x}+1$
224.1-a3
224.1-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.1
\( 2^{5} \cdot 7 \)
\( 2^{9} \cdot 7^{4} \)
$0.91464$
$(a), (-2a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$3.472144299$
1.312347190
\( -\frac{1482409}{49} a + \frac{341346}{7} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -7 a + 1\) , \( -6 a + 11\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a+1\right){x}-6a+11$
224.1-a4
224.1-a
$4$
$4$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.1
\( 2^{5} \cdot 7 \)
\( 2^{12} \cdot 7 \)
$0.91464$
$(a), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$3.472144299$
1.312347190
\( \frac{9225207}{7} a + \frac{485654}{7} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -12 a + 6\) , \( 14 a - 13\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-12a+6\right){x}+14a-13$
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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.