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-b3
7.1-b
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
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
\( -\frac{52244506558836009}{7} a + 36477727932544988 \)
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 422 a - 2086\) , \( 11275 a - 55139\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(422a-2086\right){x}+11275a-55139$
7.1-c3
7.1-c
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
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
\( -\frac{52244506558836009}{7} a + 36477727932544988 \)
\( \bigl[1\) , \( a\) , \( 1\) , \( -111 a - 475\) , \( 1218 a + 4916\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-111a-475\right){x}+1218a+4916$
49.1-c3
49.1-c
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
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
\( -\frac{52244506558836009}{7} a + 36477727932544988 \)
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 243 a - 1988\) , \( -7396 a + 26043\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(243a-1988\right){x}-7396a+26043$
49.1-e3
49.1-e
$4$
$6$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
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
\( -\frac{52244506558836009}{7} a + 36477727932544988 \)
\( \bigl[a\) , \( a\) , \( 0\) , \( -7264 a - 28276\) , \( 679453 a + 2641275\bigr] \)
${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-7264a-28276\right){x}+679453a+2641275$
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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.