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
224.2-a1
224.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.2
\( 2^{5} \cdot 7 \)
\( 2^{13} \cdot 7 \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$1.956842684$
1.479234028
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -22 a + 87\) , \( -162 a - 91\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-22a+87\right){x}-162a-91$
224.2-a2
224.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.2
\( 2^{5} \cdot 7 \)
\( 2^{5} \cdot 7^{2} \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$3.913685369$
1.479234028
\( -\frac{13647889}{14} a - \frac{40536829}{7} \)
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -3 a - 12\) , \( 23\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a-12\right){x}+23$
224.2-a3
224.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.2
\( 2^{5} \cdot 7 \)
\( 2^{14} \cdot 7^{2} \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$3.913685369$
1.479234028
\( -\frac{1145925}{112} a - \frac{72257}{56} \)
\( \bigl[a\) , \( -1\) , \( a\) , \( -2 a + 7\) , \( -2 a - 3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-2a+7\right){x}-2a-3$
224.2-a4
224.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.2
\( 2^{5} \cdot 7 \)
\( 2^{19} \cdot 7 \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{5} \)
$1$
$3.913685369$
1.479234028
\( -\frac{138325}{1792} a - \frac{317937}{896} \)
\( \bigl[a\) , \( a\) , \( a\) , \( -2\) , \( -2 a + 3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}-2{x}-2a+3$
224.2-a5
224.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.2
\( 2^{5} \cdot 7 \)
\( 2^{11} \cdot 7^{8} \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.956842684$
1.479234028
\( -\frac{5786513}{4802} a + \frac{263001}{343} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -8 a - 1\) , \( 10 a + 3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-8a-1\right){x}+10a+3$
224.2-a6
224.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.2
\( 2^{5} \cdot 7 \)
\( 2^{10} \cdot 7^{4} \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$3.913685369$
1.479234028
\( \frac{361845}{196} a - \frac{43727}{98} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 2 a - 1\) , \( 2 a - 1\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(2a-1\right){x}+2a-1$
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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.