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
784.2-a1
784.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{13} \cdot 7^{7} \)
$1.25103$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$0.739617014$
1.118195819
\( \frac{4096655365}{28} a - \frac{2878658051}{14} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 149 a - 597\) , \( 1964 a - 5468\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(149a-597\right){x}+1964a-5468$
784.2-a2
784.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{5} \cdot 7^{8} \)
$1.25103$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.479234028$
1.118195819
\( -\frac{13647889}{14} a - \frac{40536829}{7} \)
\( \bigl[a\) , \( a\) , \( 0\) , \( 16 a + 81\) , \( -205 a + 210\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(16a+81\right){x}-205a+210$
784.2-a3
784.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{14} \cdot 7^{8} \)
$1.25103$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$1.479234028$
1.118195819
\( -\frac{1145925}{112} a - \frac{72257}{56} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 9 a - 37\) , \( 32 a - 92\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(9a-37\right){x}+32a-92$
784.2-a4
784.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{19} \cdot 7^{7} \)
$1.25103$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.479234028$
1.118195819
\( -\frac{138325}{1792} a - \frac{317937}{896} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( -3 a + 15\) , \( -26 a - 14\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-3a+15\right){x}-26a-14$
784.2-a5
784.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{11} \cdot 7^{14} \)
$1.25103$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{3} \)
$1$
$0.739617014$
1.118195819
\( -\frac{5786513}{4802} a + \frac{263001}{343} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( 52 a + 15\) , \( -107 a + 305\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(52a+15\right){x}-107a+305$
784.2-a6
784.2-a
$6$
$8$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
784.2
\( 2^{4} \cdot 7^{2} \)
\( 2^{10} \cdot 7^{10} \)
$1.25103$
$(a), (-a+1), (-2a+1)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2Cs
$1$
\( 2^{4} \)
$1$
$1.479234028$
1.118195819
\( \frac{361845}{196} a - \frac{43727}{98} \)
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -18 a + 15\) , \( 5 a + 53\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-18a+15\right){x}+5a+53$
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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.