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
1.1-a1
1.1-a
$4$
$14$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.78412$
$\textsf{none}$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$11$
11Ns.3.1
$1$
\( 1 \)
$1$
$26.16385905$
0.745412115
\( -3375 \)
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2 a + 7\) , \( -a + 7\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+7\right){x}-a+7$
1.1-a2
1.1-a
$4$
$14$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
1.1
\( 1 \)
\( 1 \)
$0.78412$
$\textsf{none}$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$11$
11Ns.3.1
$1$
\( 1 \)
$1$
$26.16385905$
0.745412115
\( -3375 \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2 a + 4\) , \( 3 a + 10\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(2a+4\right){x}+3a+10$
49.1-d1
49.1-d
$4$
$14$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$2.07459$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$7, 11$
7B.1.5 , 11Ns.2.1
$1$
\( 2 \)
$5.233537470$
$3.737694151$
2.229224134
\( -3375 \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$
49.1-d2
49.1-d
$4$
$14$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
49.1
\( 7^{2} \)
\( 7^{6} \)
$2.07459$
$(a+3)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
✓
$7, 11$
7B.1.2 , 11Ns.2.1
$1$
\( 2 \)
$0.747648210$
$26.16385905$
2.229224134
\( -3375 \)
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -18 a - 71\) , \( 62 a + 240\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-18a-71\right){x}+62a+240$
81.1-a1
81.1-a
$4$
$14$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$2.35237$
$(3)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$11$
11Ns.2.1
$1$
\( 2^{2} \)
$1$
$8.721286352$
0.993882820
\( -3375 \)
\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -5 a - 3\) , \( -8 a - 21\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-3\right){x}-8a-21$
81.1-a2
81.1-a
$4$
$14$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
81.1
\( 3^{4} \)
\( 3^{12} \)
$2.35237$
$(3)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$11$
11Ns.2.1
$1$
\( 2^{2} \)
$1$
$8.721286352$
0.993882820
\( -3375 \)
\( \bigl[a + 1\) , \( 1\) , \( a\) , \( 5 a - 8\) , \( 13 a - 37\bigr] \)
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(5a-8\right){x}+13a-37$
256.1-b1
256.1-b
$4$
$14$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{24} \)
$3.13649$
$(2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$11$
11Ns.2.1
$4$
\( 2^{2} \)
$1$
$6.540964764$
2.981648460
\( -3375 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 5 a - 25\) , \( 16 a - 78\bigr] \)
${y}^2={x}^{3}+\left(5a-25\right){x}+16a-78$
256.1-b2
256.1-b
$4$
$14$
\(\Q(\sqrt{77}) \)
$2$
$[2, 0]$
256.1
\( 2^{8} \)
\( 2^{24} \)
$3.13649$
$(2)$
0
$\Z/2\Z$
$\textsf{potential}$
$-7$
$N(\mathrm{U}(1))$
✓
✓
$11$
11Ns.2.1
$4$
\( 2^{2} \)
$1$
$6.540964764$
2.981648460
\( -3375 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5 a - 20\) , \( -16 a - 62\bigr] \)
${y}^2={x}^{3}+\left(-5a-20\right){x}-16a-62$
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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.