| 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 |
| 6912.3-a1 |
6912.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{22} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.859743848$ |
$0.524717144$ |
2.760090861 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -32 a - 16\) , \( -180 a - 900\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32a-16\right){x}-180a-900$ |
| 6912.3-a2 |
6912.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.929871924$ |
$4.197737158$ |
2.760090861 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-1\right){x}$ |
| 6912.3-a3 |
6912.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{10} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.464935962$ |
$2.098868579$ |
2.760090861 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a + 4\) , \( 4 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a+4\right){x}+4a+20$ |
| 6912.3-a4 |
6912.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.929871924$ |
$1.049434289$ |
2.760090861 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 48 a + 24\) , \( -36 a - 180\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(48a+24\right){x}-36a-180$ |
| 6912.3-a5 |
6912.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{26} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.719487697$ |
$0.262358572$ |
2.760090861 |
\( -\frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -952 a + 784\) , \( -548 a - 23908\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-952a+784\right){x}-548a-23908$ |
| 6912.3-a6 |
6912.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{23} \cdot 3^{26} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.929871924$ |
$0.262358572$ |
2.760090861 |
\( \frac{2327042746553}{43046721} a + \frac{2081263802600}{43046721} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -392 a - 1456\) , \( -8388 a - 20772\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-392a-1456\right){x}-8388a-20772$ |
| 6912.3-a7 |
6912.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.929871924$ |
$1.049434289$ |
2.760090861 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 128 a + 64\) , \( 220 a + 1100\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(128a+64\right){x}+220a+1100$ |
| 6912.3-a8 |
6912.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{22} \cdot 3^{10} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.859743848$ |
$0.524717144$ |
2.760090861 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 768 a + 384\) , \( -2772 a - 13860\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(768a+384\right){x}-2772a-13860$ |
| 6912.3-b1 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{11} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.484034997$ |
1.369057715 |
\( -\frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -64 a + 1408\) , \( 13872 a + 2368\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-64a+1408\right){x}+13872a+2368$ |
| 6912.3-b2 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{11} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.484034997$ |
1.369057715 |
\( \frac{15347957750}{81} a - \frac{35138997500}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 576 a - 1152\) , \( 12092 a - 12292\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(576a-1152\right){x}+12092a-12292$ |
| 6912.3-b3 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.936139989$ |
1.369057715 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 2\) , \( 12 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-2\right){x}+12a-8$ |
| 6912.3-b4 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{23} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.484034997$ |
1.369057715 |
\( -\frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 136 a - 112\) , \( -628 a - 292\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(136a-112\right){x}-628a-292$ |
| 6912.3-b5 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{23} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.484034997$ |
1.369057715 |
\( \frac{56997401750}{43046721} a + \frac{87757407500}{43046721} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 56 a + 208\) , \( -528 a + 928\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(56a+208\right){x}-528a+928$ |
| 6912.3-b6 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.968069994$ |
1.369057715 |
\( -\frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 88\) , \( 192 a + 64\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+88\right){x}+192a+64$ |
| 6912.3-b7 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.968069994$ |
1.369057715 |
\( \frac{100738000}{6561} a + \frac{45365000}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 36 a - 72\) , \( 212 a - 196\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(36a-72\right){x}+212a-196$ |
| 6912.3-b8 |
6912.3-b |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{10} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.936139989$ |
1.369057715 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -24 a - 12\) , \( -58 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24a-12\right){x}-58a+2$ |
| 6912.3-c1 |
6912.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{15} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.384647931$ |
0.979093942 |
\( \frac{335248}{729} a + \frac{350000}{729} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a - 18\) , \( -26 a - 14\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a-18\right){x}-26a-14$ |
| 6912.3-c2 |
6912.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{12} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$2.769295863$ |
0.979093942 |
\( -\frac{48640}{27} a + \frac{74752}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 7\) , \( -7 a\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+7\right){x}-7a$ |
| 6912.3-d1 |
6912.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{5} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.942357452$ |
2.080560907 |
\( -\frac{167792}{9} a - \frac{21616}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 6\) , \( -2 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+6\right){x}-2a+10$ |
| 6912.3-d2 |
6912.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$5.884714905$ |
2.080560907 |
\( \frac{3584}{3} a + \frac{4096}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -a + 1\) , \( -a\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}-a$ |
| 6912.3-e1 |
6912.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.110473379$ |
1.570446513 |
\( -\frac{41803784}{9} a - \frac{21890312}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -32 a - 160\) , \( 272 a + 680\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32a-160\right){x}+272a+680$ |
| 6912.3-e2 |
6912.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.110473379$ |
1.570446513 |
\( \frac{41803784}{9} a - \frac{21890312}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -96 a + 96\) , \( -148 a - 844\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-96a+96\right){x}-148a-844$ |
| 6912.3-e3 |
6912.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{15} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.110473379$ |
1.570446513 |
\( -\frac{27471928}{6561} a - \frac{56129704}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 28 a - 40\) , \( 140 a - 52\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(28a-40\right){x}+140a-52$ |
| 6912.3-e4 |
6912.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{15} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.110473379$ |
1.570446513 |
\( \frac{27471928}{6561} a - \frac{56129704}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a + 56\) , \( 104 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a+56\right){x}+104a-16$ |
| 6912.3-e5 |
6912.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{12} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.220946758$ |
1.570446513 |
\( -\frac{121088}{81} a - \frac{65728}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 6\) , \( -4 a - 16\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+6\right){x}-4a-16$ |
| 6912.3-e6 |
6912.3-e |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{12} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.220946758$ |
1.570446513 |
\( \frac{121088}{81} a - \frac{65728}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 10\) , \( 8 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-10\right){x}+8a+8$ |
| 6912.3-f1 |
6912.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.231276517$ |
$2.397245973$ |
3.136311034 |
\( -\frac{9472}{9} a - \frac{71552}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a + 11\) , \( 7 a + 7\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+11\right){x}+7a+7$ |
| 6912.3-f2 |
6912.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{19} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.925106069$ |
$1.198622986$ |
3.136311034 |
\( \frac{15609244}{6561} a - \frac{20009248}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 40\) , \( 4 a + 100\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-40\right){x}+4a+100$ |
| 6912.3-f3 |
6912.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{10} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$0.462553034$ |
$2.397245973$ |
3.136311034 |
\( -\frac{39872}{81} a - \frac{110368}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a\) , \( -8 a + 4\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-6a{x}-8a+4$ |
| 6912.3-f4 |
6912.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{19} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.925106069$ |
$1.198622986$ |
3.136311034 |
\( \frac{18653188}{9} a + \frac{32152304}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -96 a\) , \( -332 a + 364\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-96a{x}-332a+364$ |
| 6912.3-g1 |
6912.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.677048354$ |
1.914981930 |
\( -\frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -156 a - 168\) , \( -1224 a - 504\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-156a-168\right){x}-1224a-504$ |
| 6912.3-g2 |
6912.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.677048354$ |
1.914981930 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -196 a - 8\) , \( 856 a - 1336\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-196a-8\right){x}+856a-1336$ |
| 6912.3-g3 |
6912.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.354096709$ |
1.914981930 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -16 a - 8\) , \( -8 a - 40\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16a-8\right){x}-8a-40$ |
| 6912.3-g4 |
6912.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{10} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$2.708193418$ |
1.914981930 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a+2\right){x}$ |
| 6912.3-g5 |
6912.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.708193418$ |
1.914981930 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a + 4\) , \( -2 a - 10\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(8a+4\right){x}-2a-10$ |
| 6912.3-g6 |
6912.3-g |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.354096709$ |
1.914981930 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 64 a + 32\) , \( -60 a - 300\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(64a+32\right){x}-60a-300$ |
| 6912.3-h1 |
6912.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.265468825$ |
$0.677048354$ |
4.066944035 |
\( -\frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -156 a - 168\) , \( 1224 a + 504\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-156a-168\right){x}+1224a+504$ |
| 6912.3-h2 |
6912.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{21} \cdot 3^{16} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.061875302$ |
$0.677048354$ |
4.066944035 |
\( \frac{1056226562}{6561} a - \frac{605268760}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -196 a - 8\) , \( -856 a + 1336\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-196a-8\right){x}-856a+1336$ |
| 6912.3-h3 |
6912.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.530937651$ |
$1.354096709$ |
4.066944035 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -16 a - 8\) , \( 8 a + 40\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a-8\right){x}+8a+40$ |
| 6912.3-h4 |
6912.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{10} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.061875302$ |
$2.708193418$ |
4.066944035 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+2\right){x}$ |
| 6912.3-h5 |
6912.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.123750605$ |
$2.708193418$ |
4.066944035 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8 a + 4\) , \( 2 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(8a+4\right){x}+2a+10$ |
| 6912.3-h6 |
6912.3-h |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.530937651$ |
$1.354096709$ |
4.066944035 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 64 a + 32\) , \( 60 a + 300\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(64a+32\right){x}+60a+300$ |
| 6912.3-i1 |
6912.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{16} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.612657711$ |
$2.397245973$ |
4.154086116 |
\( -\frac{9472}{9} a - \frac{71552}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -2 a + 11\) , \( -7 a - 7\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+11\right){x}-7a-7$ |
| 6912.3-i2 |
6912.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{19} \cdot 3^{14} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.153164427$ |
$1.198622986$ |
4.154086116 |
\( \frac{15609244}{6561} a - \frac{20009248}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a - 40\) , \( -4 a - 100\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a-40\right){x}-4a-100$ |
| 6912.3-i3 |
6912.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{14} \cdot 3^{10} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.306328855$ |
$2.397245973$ |
4.154086116 |
\( -\frac{39872}{81} a - \frac{110368}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -6 a\) , \( 8 a - 4\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-6a{x}+8a-4$ |
| 6912.3-i4 |
6912.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{19} \cdot 3^{8} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.612657711$ |
$1.198622986$ |
4.154086116 |
\( \frac{18653188}{9} a + \frac{32152304}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -96 a\) , \( 332 a - 364\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-96a{x}+332a-364$ |
| 6912.3-j1 |
6912.3-j |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.767134476$ |
$1.110473379$ |
4.345636691 |
\( -\frac{41803784}{9} a - \frac{21890312}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -32 a - 160\) , \( -272 a - 680\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-32a-160\right){x}-272a-680$ |
| 6912.3-j2 |
6912.3-j |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{9} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.383567238$ |
$1.110473379$ |
4.345636691 |
\( \frac{41803784}{9} a - \frac{21890312}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -96 a + 96\) , \( 148 a + 844\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-96a+96\right){x}+148a+844$ |
| 6912.3-j3 |
6912.3-j |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{15} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.691783619$ |
$1.110473379$ |
4.345636691 |
\( -\frac{27471928}{6561} a - \frac{56129704}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 28 a - 40\) , \( -140 a + 52\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(28a-40\right){x}-140a+52$ |
| 6912.3-j4 |
6912.3-j |
$6$ |
$8$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
6912.3 |
\( 2^{8} \cdot 3^{3} \) |
\( 2^{18} \cdot 3^{15} \) |
$2.30454$ |
$(a), (-a-1), (a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.345891809$ |
$1.110473379$ |
4.345636691 |
\( \frac{27471928}{6561} a - \frac{56129704}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a + 56\) , \( -104 a + 16\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+56\right){x}-104a+16$ |
*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.
