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
7.1-a1
7.1-a
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( -7 \)
$1.27544$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$39.11307331$
1.114337095
\( -\frac{152807671423}{7} a + \frac{745053380628}{7} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 116 a - 566\) , \( -1240 a + 6064\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(116a-566\right){x}-1240a+6064$
7.1-d1
7.1-d
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( -7 \)
$1.27544$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 1 \)
$20.23046162$
$1.535139138$
1.769612505
\( -\frac{152807671423}{7} a + \frac{745053380628}{7} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24 a - 109\) , \( -229 a - 919\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-24a-109\right){x}-229a-919$
49.1-a1
49.1-a
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( - 7^{7} \)
$2.07459$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2 \)
$7.801344256$
$3.575708421$
3.178968155
\( -\frac{152807671423}{7} a + \frac{745053380628}{7} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 72 a - 520\) , \( 1215 a - 5391\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(72a-520\right){x}+1215a-5391$
49.1-b1
49.1-b
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( - 7^{7} \)
$2.07459$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$5.516963282$
$2.398885662$
3.016437112
\( -\frac{152807671423}{7} a + \frac{745053380628}{7} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1657 a - 6449\) , \( -73928 a - 287391\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1657a-6449\right){x}-73928a-287391$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.