| 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 |
| 1024.1-c1 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$1.67652$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.518236630 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.99373$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.732897270 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^3-4{x}$ |
| 64.1-b1 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-33}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \cdot 3^{12} \) |
$2.90383$ |
$(2,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$6.875185818$ |
1.196816231 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \) |
${y}^2={x}^3-9{x}$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-66}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \cdot 11^{12} \) |
$3.45325$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$0.888625874$ |
$6.875185818$ |
1.504047053 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -121\) , \( 0\bigr] \) |
${y}^2={x}^3-121{x}$ |
| 64.1-b1 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-77}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \cdot 7^{12} \) |
$4.43567$ |
$(2,a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2 \) |
$2.988881507$ |
$6.875185818$ |
2.341789076 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -49\) , \( 0\bigr] \) |
${y}^2={x}^3-49{x}$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-110}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \cdot 11^{12} \) |
$4.45813$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$16$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.311046494 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -121\) , \( 0\bigr] \) |
${y}^2={x}^3-121{x}$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-154}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \cdot 11^{12} \) |
$5.27493$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$2.134120849$ |
$13.75037163$ |
2.364683844 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -121\) , \( 0\bigr] \) |
${y}^2={x}^3-121{x}$ |
| 64.1-a1 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-209}) \) |
$2$ |
$[0, 1]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \cdot 11^{12} \) |
$7.30780$ |
$(2,a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2^{2} \) |
$1$ |
$13.75037163$ |
0.475566547 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -121\) , \( 0\bigr] \) |
${y}^2={x}^3-121{x}$ |
| 64.1-b1 |
64.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{11}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{12} \) |
$1.67652$ |
$(a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$27.50074327$ |
0.518236630 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{22}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.99373$ |
$(-3a-14)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$27.50074327$ |
0.732897270 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16548 a - 77617\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-16548a-77617\right){x}$ |
*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.
