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
224.5-a1
224.5-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.5
\( 2^{5} \cdot 7 \)
\( 2^{13} \cdot 7 \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$4$
\( 2^{2} \)
$1$
$1.956842684$
1.479234028
\( -\frac{4096655365}{28} a - \frac{1660660737}{28} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 20 a + 65\) , \( 161 a - 253\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a+65\right){x}+161a-253$
224.5-a2
224.5-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.5
\( 2^{5} \cdot 7 \)
\( 2^{5} \cdot 7^{2} \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2 \)
$1$
$3.913685369$
1.479234028
\( \frac{13647889}{14} a - \frac{94721547}{14} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3 a - 16\) , \( -12 a + 18\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(3a-16\right){x}-12a+18$
224.5-a3
224.5-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.5
\( 2^{5} \cdot 7 \)
\( 2^{14} \cdot 7^{2} \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{5} \)
$1$
$3.913685369$
1.479234028
\( \frac{1145925}{112} a - \frac{1290439}{112} \)
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 5\) , \( a - 5\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+5{x}+a-5$
224.5-a4
224.5-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.5
\( 2^{5} \cdot 7 \)
\( 2^{19} \cdot 7 \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{5} \)
$1$
$3.913685369$
1.479234028
\( \frac{138325}{1792} a - \frac{774199}{1792} \)
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3\) , \( -a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}-3{x}-a+1$
224.5-a5
224.5-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.5
\( 2^{5} \cdot 7 \)
\( 2^{11} \cdot 7^{8} \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.956842684$
1.479234028
\( \frac{5786513}{4802} a - \frac{2104499}{4802} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 6 a - 9\) , \( -11 a + 13\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-9\right){x}-11a+13$
224.5-a6
224.5-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
224.5
\( 2^{5} \cdot 7 \)
\( 2^{10} \cdot 7^{4} \)
$0.91464$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$3.913685369$
1.479234028
\( -\frac{361845}{196} a + \frac{274391}{196} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -4 a + 1\) , \( -3 a + 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+1\right){x}-3a+1$
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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.