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-a2
7.1-a
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( - 7^{3} \)
$1.27544$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 1 \)
$1$
$39.11307331$
1.114337095
\( -\frac{37367}{49} a + \frac{175235}{49} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( a - 1\) , \( -2\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}-2$
7.1-d2
7.1-d
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( - 7^{3} \)
$1.27544$
$(a+3)$
$1$
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.1
$1$
\( 3 \)
$6.743487207$
$13.81625224$
1.769612505
\( -\frac{37367}{49} a + \frac{175235}{49} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\) , \( a + 2\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}+a+2$
49.1-a2
49.1-a
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( - 7^{9} \)
$2.07459$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2 \)
$2.600448085$
$10.72712526$
3.178968155
\( -\frac{37367}{49} a + \frac{175235}{49} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( 2 a + 5\) , \( 4 a - 8\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(2a+5\right){x}+4a-8$
49.1-b2
49.1-b
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( - 7^{9} \)
$2.07459$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$1.838987760$
$7.196656988$
3.016437112
\( -\frac{37367}{49} a + \frac{175235}{49} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -12 a - 44\) , \( -162 a - 629\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-12a-44\right){x}-162a-629$
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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.