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-a4
7.1-a
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( 7^{2} \)
$1.27544$
$(a+3)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B
$1$
\( 2 \)
$1$
$19.55653665$
1.114337095
\( \frac{52244506558836009}{7} a + \frac{203099588968978907}{7} \)
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 111 a - 586\) , \( -1218 a + 6134\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(111a-586\right){x}-1218a+6134$
7.1-d4
7.1-d
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
7.1
\( 7 \)
\( 7^{2} \)
$1.27544$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2, 3$
2B , 3B.1.2
$1$
\( 2 \)
$10.11523081$
$1.535139138$
1.769612505
\( \frac{52244506558836009}{7} a + \frac{203099588968978907}{7} \)
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -424 a - 1664\) , \( -11276 a - 43864\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-424a-1664\right){x}-11276a-43864$
49.1-a4
49.1-a
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{8} \)
$2.07459$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$3.900672128$
$3.575708421$
3.178968155
\( \frac{52244506558836009}{7} a + \frac{203099588968978907}{7} \)
\( \bigl[a\) , \( 1\) , \( 0\) , \( -243 a - 1745\) , \( 7396 a + 18647\bigr] \)
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-243a-1745\right){x}+7396a+18647$
49.1-b4
49.1-b
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{8} \)
$2.07459$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B
$1$
\( 2^{2} \)
$11.03392656$
$1.199442831$
3.016437112
\( \frac{52244506558836009}{7} a + \frac{203099588968978907}{7} \)
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 7276 a - 35531\) , \( -707728 a + 3458853\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7276a-35531\right){x}-707728a+3458853$
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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.