| 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 |
| 32.1-a3 |
32.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$0.60113$ |
$(a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$13.75037163$ |
0.607686314 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 32.1-a4 |
32.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$0.60113$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$27.50074327$ |
0.607686314 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 256.1-a3 |
256.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.01098$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$13.75037163$ |
1.215372628 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a+3\right){x}$ |
| 256.1-a4 |
256.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{12} \) |
$1.01098$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$27.50074327$ |
1.215372628 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-3\right){x}$ |
| 1024.1-f3 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.718796454 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+6\right){x}$ |
| 1024.1-f4 |
1024.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$19.44596205$ |
1.718796454 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 6\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-6\right){x}$ |
| 1024.1-k3 |
1024.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.304354515$ |
$9.722981027$ |
2.092493851 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+2{x}$ |
| 1024.1-k4 |
1024.1-k |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.42974$ |
$(a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.608709031$ |
$19.44596205$ |
2.092493851 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-2{x}$ |
| 1568.2-c1 |
1568.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.518620871$ |
1.597573729 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a - 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-16a-13\right){x}$ |
| 1568.2-c2 |
1568.2-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.518620871$ |
1.597573729 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(16a+13\right){x}$ |
| 1568.2-g1 |
1568.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.294548727$ |
$11.95514709$ |
2.489986982 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+5\right){x}$ |
| 1568.2-g2 |
1568.2-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.59045$ |
$(a), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.147274363$ |
$11.95514709$ |
2.489986982 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-5\right){x}$ |
| 1568.2-i3 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.197151969$ |
1.837470700 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+9\right){x}$ |
| 1568.2-i4 |
1568.2-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.2 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.59045$ |
$(a), (-2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.39430393$ |
1.837470700 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-9\right){x}$ |
| 1568.3-c1 |
1568.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.3 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1.59045$ |
$(a), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.518620871$ |
1.597573729 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(16a-13\right){x}$ |
| 1568.3-c2 |
1568.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.3 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{9} \) |
$1.59045$ |
$(a), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.518620871$ |
1.597573729 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 13\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-16a+13\right){x}$ |
| 1568.3-g1 |
1568.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.3 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.59045$ |
$(a), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.294548727$ |
$11.95514709$ |
2.489986982 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+5\right){x}$ |
| 1568.3-g2 |
1568.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.3 |
\( 2^{5} \cdot 7^{2} \) |
\( - 2^{12} \cdot 7^{3} \) |
$1.59045$ |
$(a), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.147274363$ |
$11.95514709$ |
2.489986982 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-5\right){x}$ |
| 1568.3-i3 |
1568.3-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.3 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.59045$ |
$(a), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.197151969$ |
1.837470700 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+9\right){x}$ |
| 1568.3-i4 |
1568.3-i |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1568.3 |
\( 2^{5} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.59045$ |
$(a), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.39430393$ |
1.837470700 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-9\right){x}$ |
| 2592.1-c1 |
2592.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2592.1 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.80340$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$5.292520510$ |
1.871188571 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -27\) , \( 0\bigr] \) |
${y}^2={x}^{3}-27{x}$ |
| 2592.1-c2 |
2592.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2592.1 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.80340$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$2.646260255$ |
1.871188571 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 27\) , \( 0\bigr] \) |
${y}^2={x}^{3}+27{x}$ |
| 2592.1-d3 |
2592.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2592.1 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.80340$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.444312937$ |
$4.583457212$ |
2.880030840 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 0\bigr] \) |
${y}^2={x}^{3}+9{x}$ |
| 2592.1-d4 |
2592.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2592.1 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{12} \) |
$1.80340$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.888625874$ |
$9.166914424$ |
2.880030840 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \) |
${y}^2={x}^{3}-9{x}$ |
| 2592.1-f1 |
2592.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2592.1 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.250591196$ |
$15.87756153$ |
2.813420292 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2={x}^{3}-3{x}$ |
| 2592.1-f2 |
2592.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2592.1 |
\( 2^{5} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.80340$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.501182392$ |
$7.938780765$ |
2.813420292 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+3{x}$ |
| 4096.1-e1 |
4096.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{18} \) |
$2.02196$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.670654900$ |
$13.75037163$ |
3.260382434 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a+2\right){x}$ |
| 4096.1-e2 |
4096.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{18} \) |
$2.02196$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.335327450$ |
$13.75037163$ |
3.260382434 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-2\right){x}$ |
| 4096.1-f1 |
4096.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{12} \) |
$2.02196$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$19.44596205$ |
1.718796454 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}$ |
| 4096.1-f2 |
4096.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{12} \) |
$2.02196$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$19.44596205$ |
1.718796454 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}$ |
| 4096.1-g1 |
4096.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{18} \) |
$2.02196$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.670654900$ |
$13.75037163$ |
3.260382434 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a+2\right){x}$ |
| 4096.1-g2 |
4096.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{18} \) |
$2.02196$ |
$(a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.335327450$ |
$13.75037163$ |
3.260382434 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-2\right){x}$ |
| 4096.1-h1 |
4096.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{12} \) |
$2.02196$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$19.44596205$ |
1.718796454 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}$ |
| 4096.1-h2 |
4096.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( - 2^{12} \) |
$2.02196$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$19.44596205$ |
1.718796454 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}$ |
*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.
