| 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 |
| 1296.1-a1 |
1296.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.898343969$ |
2.085379509 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \) |
${y}^2={x}^{3}-1$ |
| 1296.1-a2 |
1296.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.898343969$ |
2.085379509 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 27\bigr] \) |
${y}^2={x}^{3}+27$ |
| 1296.1-a3 |
1296.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$11.79668793$ |
2.085379509 |
\( 54000 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -4\) , \( -5\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-4{x}-5$ |
| 1296.1-a4 |
1296.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{18} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$11.79668793$ |
2.085379509 |
\( 54000 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -34\) , \( 57\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-34{x}+57$ |
| 1296.1-b1 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( - 2^{11} \cdot 3^{14} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$8.634190917$ |
$0.193773322$ |
2.366086572 |
\( -\frac{123062343233293457}{3} a + 58012144939294440 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 4590 a - 7344\) , \( 220212 a - 321908\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(4590a-7344\right){x}+220212a-321908$ |
| 1296.1-b2 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{28} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.079273864$ |
$0.775093289$ |
2.366086572 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 36\) , \( -572\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+36{x}-572$ |
| 1296.1-b3 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.539636932$ |
$6.200746317$ |
2.366086572 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \) |
${y}^2={x}^{3}+6{x}+7$ |
| 1296.1-b4 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{4} \cdot 3^{16} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.079273864$ |
$12.40149263$ |
2.366086572 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -9\) , \( 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-9{x}+4$ |
| 1296.1-b5 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{20} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.158547729$ |
$3.100373158$ |
2.366086572 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -54\) , \( -176\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-54{x}-176$ |
| 1296.1-b6 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{14} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.539636932$ |
$12.40149263$ |
2.366086572 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -144\) , \( 598\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-144{x}+598$ |
| 1296.1-b7 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{10} \cdot 3^{16} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$4.317095458$ |
$0.775093289$ |
2.366086572 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -864\) , \( -10220\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}-864{x}-10220$ |
| 1296.1-b8 |
1296.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( - 2^{11} \cdot 3^{14} \) |
$1.51647$ |
$(a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$8.634190917$ |
$0.193773322$ |
2.366086572 |
\( \frac{123062343233293457}{3} a + 58012144939294440 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -4590 a - 7344\) , \( -220212 a - 321908\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-4590a-7344\right){x}-220212a-321908$ |
| 1296.1-c1 |
1296.1-c |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{32} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$0.211153890$ |
1.866354347 |
\( -\frac{873722816}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1434 a - 2151\) , \( 38654 a - 55220\bigr] \) |
${y}^2={x}^{3}+\left(1434a-2151\right){x}+38654a-55220$ |
| 1296.1-c2 |
1296.1-c |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{16} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$5.278847260$ |
1.866354347 |
\( \frac{64}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a + 9\) , \( 154 a + 220\bigr] \) |
${y}^2={x}^{3}+\left(6a+9\right){x}+154a+220$ |
| 1296.1-c3 |
1296.1-c |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{14} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$10.55769452$ |
1.866354347 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -66 a - 99\) , \( 350 a + 500\bigr] \) |
${y}^2={x}^{3}+\left(-66a-99\right){x}+350a+500$ |
| 1296.1-c4 |
1296.1-c |
$4$ |
$10$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{22} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$0.422307780$ |
1.866354347 |
\( \frac{58591911104}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -5826 a - 8739\) , \( -299530 a - 427900\bigr] \) |
${y}^2={x}^{3}+\left(-5826a-8739\right){x}-299530a-427900$ |
| 1296.1-d1 |
1296.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-24$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.651613565$ |
1.175850264 |
\( -1707264 a + 2417472 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a - 15\) , \( 14 a - 24\bigr] \) |
${y}^2={x}^{3}+\left(6a-15\right){x}+14a-24$ |
| 1296.1-d2 |
1296.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-24$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.651613565$ |
1.175850264 |
\( -1707264 a + 2417472 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 54 a - 135\) , \( -378 a + 648\bigr] \) |
${y}^2={x}^{3}+\left(54a-135\right){x}-378a+648$ |
| 1296.1-d3 |
1296.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-24$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.651613565$ |
1.175850264 |
\( 1707264 a + 2417472 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 a - 15\) , \( -14 a - 24\bigr] \) |
${y}^2={x}^{3}+\left(-6a-15\right){x}-14a-24$ |
| 1296.1-d4 |
1296.1-d |
$4$ |
$6$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
1296.1 |
\( 2^{4} \cdot 3^{4} \) |
\( 2^{12} \cdot 3^{18} \) |
$1.51647$ |
$(a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-24$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.651613565$ |
1.175850264 |
\( 1707264 a + 2417472 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -54 a - 135\) , \( 378 a + 648\bigr] \) |
${y}^2={x}^{3}+\left(-54a-135\right){x}+378a+648$ |
*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.
