| 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 |
| 4096.1-a1 |
4096.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.831641843 |
\( 8000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 2\) , \( 3 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}+3a+5$ |
| 4096.1-a2 |
4096.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.831641843 |
\( 8000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( a - 2\) , \( -3 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(a-2\right){x}-3a+5$ |
| 4096.1-b1 |
4096.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.162411742$ |
$31.09162971$ |
5.216543780 |
\( -241408 a + 420032 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 21 a - 34\) , \( -61 a + 105\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(21a-34\right){x}-61a+105$ |
| 4096.1-b2 |
4096.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$2.324823485$ |
$15.54581485$ |
5.216543780 |
\( 241408 a + 420032 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -a - 3\) , \( -a - 1\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-a-3\right){x}-a-1$ |
| 4096.1-c1 |
4096.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.608709031$ |
$19.44596205$ |
3.417028151 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^{3}-2{x}$ |
| 4096.1-c2 |
4096.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.217418063$ |
$9.722981027$ |
3.417028151 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 14\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-8a+14\right){x}$ |
| 4096.1-d1 |
4096.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.137558362$ |
$23.86007700$ |
3.789903971 |
\( -241408 a + 420032 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 10 a - 18\) , \( -16 a + 28\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(10a-18\right){x}-16a+28$ |
| 4096.1-d2 |
4096.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.137558362$ |
$23.86007700$ |
3.789903971 |
\( 241408 a + 420032 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 48 a - 83\) , \( -56 a + 97\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(48a-83\right){x}-56a+97$ |
| 4096.1-e1 |
4096.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.12873342$ |
2.923913485 |
\( -241408 a + 420032 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10 a - 18\) , \( 16 a - 28\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-18\right){x}+16a-28$ |
| 4096.1-e2 |
4096.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$10.12873342$ |
2.923913485 |
\( 241408 a + 420032 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 48 a - 83\) , \( 56 a - 97\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(48a-83\right){x}+56a-97$ |
| 4096.1-f1 |
4096.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.916007581$ |
$27.50074327$ |
3.635991684 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-2\right){x}$ |
| 4096.1-f2 |
4096.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.832015163$ |
$13.75037163$ |
3.635991684 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+2\right){x}$ |
| 4096.1-g1 |
4096.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.507223467$ |
$12.68998693$ |
3.716206908 |
\( 8000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 14 a - 22\) , \( 28 a - 48\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(14a-22\right){x}+28a-48$ |
| 4096.1-g2 |
4096.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.126805866$ |
$25.37997386$ |
3.716206908 |
\( 8000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}+1$ |
| 4096.1-h1 |
4096.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.260146265$ |
$15.54581485$ |
2.827573020 |
\( -241408 a + 420032 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -7 a - 10\) , \( 5 a + 9\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-10\right){x}+5a+9$ |
| 4096.1-h2 |
4096.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.630073132$ |
$31.09162971$ |
2.827573020 |
\( 241408 a + 420032 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -a - 3\) , \( a + 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-a-3\right){x}+a+1$ |
| 4096.1-i1 |
4096.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$2.324823485$ |
$15.54581485$ |
5.216543780 |
\( -241408 a + 420032 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 283 a - 490\) , \( 3161 a - 5475\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(283a-490\right){x}+3161a-5475$ |
| 4096.1-i2 |
4096.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.162411742$ |
$31.09162971$ |
5.216543780 |
\( 241408 a + 420032 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 7 a - 10\) , \( 5 a - 9\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(7a-10\right){x}+5a-9$ |
| 4096.1-j1 |
4096.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.357370674$ |
$19.44596205$ |
4.012247529 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a - 14\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(8a-14\right){x}$ |
| 4096.1-j2 |
4096.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.714741348$ |
$9.722981027$ |
4.012247529 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+2{x}$ |
| 4096.1-k1 |
4096.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.12873342$ |
1.461956742 |
\( -241408 a + 420032 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a - 6\) , \( -4 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-6\right){x}-4a-8$ |
| 4096.1-k2 |
4096.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.12873342$ |
1.461956742 |
\( 241408 a + 420032 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 6\) , \( 4 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2a-6\right){x}+4a-8$ |
| 4096.1-l1 |
4096.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$23.86007700$ |
3.443905470 |
\( -241408 a + 420032 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a - 6\) , \( 4 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-6\right){x}+4a+8$ |
| 4096.1-l2 |
4096.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$23.86007700$ |
3.443905470 |
\( 241408 a + 420032 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a - 6\) , \( -4 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-6\right){x}-4a+8$ |
| 4096.1-m1 |
4096.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.831641843 |
\( 8000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a - 2\) , \( 3 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-2\right){x}+3a-5$ |
| 4096.1-m2 |
4096.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$25.37997386$ |
1.831641843 |
\( 8000 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 25 a - 43\) , \( -71 a + 123\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(25a-43\right){x}-71a+123$ |
| 4096.1-n1 |
4096.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.916007581$ |
$27.50074327$ |
3.635991684 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a - 26\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(15a-26\right){x}$ |
| 4096.1-n2 |
4096.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.832015163$ |
$13.75037163$ |
3.635991684 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+2\right){x}$ |
| 4096.1-o1 |
4096.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$25.37997386$ |
3.663283686 |
\( 8000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a - 22\) , \( -28 a + 48\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(14a-22\right){x}-28a+48$ |
| 4096.1-o2 |
4096.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{18} \) |
$2.47639$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$12.68998693$ |
3.663283686 |
\( 8000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 186 a - 322\) , \( 1448 a - 2508\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(186a-322\right){x}+1448a-2508$ |
| 4096.1-p1 |
4096.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.630073132$ |
$31.09162971$ |
2.827573020 |
\( -241408 a + 420032 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( a - 3\) , \( -a + 1\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(a-3\right){x}-a+1$ |
| 4096.1-p2 |
4096.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.47639$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1.260146265$ |
$15.54581485$ |
2.827573020 |
\( 241408 a + 420032 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 7 a - 10\) , \( -5 a + 9\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(7a-10\right){x}-5a+9$ |
*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.
