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 |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -15 a - 40\) , \( 67 a + 177\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-15a-40\right){x}+67a+177$ |
1.1-a2 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-7$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 15 a - 40\) , \( -67 a + 177\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(15a-40\right){x}-67a+177$ |
1.1-a3 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.540964764$ |
0.309031537 |
\( -51954490735875 a + 137458661985000 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -270 a - 715\) , \( 3223 a + 8527\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-270a-715\right){x}+3223a+8527$ |
1.1-a4 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( -51954490735875 a + 137458661985000 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -270 a - 718\) , \( -3223 a - 8529\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-270a-718\right){x}-3223a-8529$ |
1.1-a5 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( 16581375 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -255 a - 678\) , \( -3669 a - 9709\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-255a-678\right){x}-3669a-9709$ |
1.1-a6 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-28$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( 16581375 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 255 a - 678\) , \( 3669 a - 9709\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(255a-678\right){x}+3669a-9709$ |
1.1-a7 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$6.540964764$ |
0.309031537 |
\( 51954490735875 a + 137458661985000 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 270 a - 715\) , \( -3223 a + 8527\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(270a-715\right){x}-3223a+8527$ |
1.1-a8 |
1.1-a |
$8$ |
$28$ |
\(\Q(\sqrt{7}) \) |
$2$ |
$[2, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$0.47284$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-112$ |
$N(\mathrm{U}(1))$ |
✓ |
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$26.16385905$ |
0.309031537 |
\( 51954490735875 a + 137458661985000 \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 270 a - 718\) , \( 3223 a - 8529\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(270a-718\right){x}+3223a-8529$ |
*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.