| 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 |
| 768.1-a1 |
768.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.233061224$ |
$11.50728806$ |
4.379528682 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( 2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+2{x}+2$ |
| 768.1-a2 |
768.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.466122448$ |
$23.01457612$ |
4.379528682 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 66 a - 161\) , \( -305 a + 747\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(66a-161\right){x}-305a+747$ |
| 768.1-b1 |
768.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.319732820$ |
$11.50728806$ |
3.004101308 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 34 a + 84\) , \( 240 a + 588\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(34a+84\right){x}+240a+588$ |
| 768.1-b2 |
768.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.159866410$ |
$23.01457612$ |
3.004101308 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-3{x}+3$ |
| 768.1-c1 |
768.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.588112610$ |
$17.63288296$ |
2.116792049 |
\( \frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+3{x}$ |
| 768.1-c2 |
768.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.294056305$ |
$17.63288296$ |
2.116792049 |
\( -\frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -12\) , \( -12 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}-12{x}-12a+12$ |
| 768.1-d1 |
768.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.63288296$ |
3.599297162 |
\( -\frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -20 a - 45\) , \( 90 a + 222\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a-45\right){x}+90a+222$ |
| 768.1-d2 |
768.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.63288296$ |
3.599297162 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 254 a - 622\) , \( 2336 a - 5722\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(254a-622\right){x}+2336a-5722$ |
| 768.1-e1 |
768.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.588112610$ |
$17.63288296$ |
2.116792049 |
\( -\frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+3{x}$ |
| 768.1-e2 |
768.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.294056305$ |
$17.63288296$ |
2.116792049 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -12\) , \( 12 a + 12\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-12{x}+12a+12$ |
| 768.1-f1 |
768.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.63288296$ |
3.599297162 |
\( \frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 20 a - 45\) , \( -90 a + 222\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-45\right){x}-90a+222$ |
| 768.1-f2 |
768.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.63288296$ |
3.599297162 |
\( -\frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -254 a - 622\) , \( -2336 a - 5722\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-254a-622\right){x}-2336a-5722$ |
| 768.1-g1 |
768.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.917567739$ |
0.782843751 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 126 a - 308\) , \( 3008 a - 7368\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(126a-308\right){x}+3008a-7368$ |
| 768.1-g2 |
768.1-g |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{6} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.835135479$ |
0.782843751 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -35\) , \( -69\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-35{x}-69$ |
| 768.1-h1 |
768.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.706985663$ |
1.369057715 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 6\) , \( -24 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a-6\right){x}-24a-60$ |
| 768.1-h2 |
768.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.41397132$ |
1.369057715 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 24 a - 56\) , \( -86 a + 210\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(24a-56\right){x}-86a+210$ |
| 768.1-i1 |
768.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.394078358$ |
$6.706985663$ |
4.316128133 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 6\) , \( -24 a + 60\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-6\right){x}-24a+60$ |
| 768.1-i2 |
768.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.788156716$ |
$13.41397132$ |
4.316128133 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -24 a - 56\) , \( -86 a - 210\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24a-56\right){x}-86a-210$ |
| 768.1-j1 |
768.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$1.917567739$ |
4.697062509 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -6\) , \( -18\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-6{x}-18$ |
| 768.1-j2 |
768.1-j |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{6} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$3.835135479$ |
4.697062509 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 706 a - 1729\) , \( 16799 a - 41149\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(706a-1729\right){x}+16799a-41149$ |
| 768.1-k1 |
768.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$6.706985663$ |
1.369057715 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 6\) , \( 24 a - 60\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-6\right){x}+24a-60$ |
| 768.1-k2 |
768.1-k |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$13.41397132$ |
1.369057715 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -24 a - 56\) , \( 86 a + 210\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-24a-56\right){x}+86a+210$ |
| 768.1-l1 |
768.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$8.807833659$ |
3.595783034 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -6\) , \( 18\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-6{x}+18$ |
| 768.1-l2 |
768.1-l |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{6} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.61566731$ |
3.595783034 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 706 a - 1729\) , \( -16799 a + 41149\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(706a-1729\right){x}-16799a+41149$ |
| 768.1-m1 |
768.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{12} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.045085921$ |
$8.807833659$ |
3.890860564 |
\( -\frac{219488}{729} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -126 a - 308\) , \( 3008 a + 7368\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-126a-308\right){x}+3008a+7368$ |
| 768.1-m2 |
768.1-m |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{6} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.045085921$ |
$17.61566731$ |
3.890860564 |
\( \frac{19056256}{27} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -35\) , \( 69\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-35{x}+69$ |
| 768.1-n1 |
768.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{8} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.394078358$ |
$6.706985663$ |
4.316128133 |
\( -\frac{8000}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 6\) , \( 24 a + 60\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-6\right){x}+24a+60$ |
| 768.1-n2 |
768.1-n |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.788156716$ |
$13.41397132$ |
4.316128133 |
\( \frac{2744000}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 24 a - 56\) , \( 86 a - 210\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(24a-56\right){x}+86a-210$ |
| 768.1-o1 |
768.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.582692143$ |
1.547810552 |
\( -\frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+3{x}$ |
| 768.1-o2 |
768.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.582692143$ |
1.547810552 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -12\) , \( -12 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-12{x}-12a-12$ |
| 768.1-p1 |
768.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.577633854$ |
$7.582692143$ |
3.989688880 |
\( \frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20 a - 45\) , \( 90 a - 222\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(20a-45\right){x}+90a-222$ |
| 768.1-p2 |
768.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.288816927$ |
$7.582692143$ |
3.989688880 |
\( -\frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -254 a - 622\) , \( 2336 a + 5722\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-254a-622\right){x}+2336a+5722$ |
| 768.1-q1 |
768.1-q |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.582692143$ |
1.547810552 |
\( \frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+3{x}$ |
| 768.1-q2 |
768.1-q |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$7.582692143$ |
1.547810552 |
\( -\frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -12\) , \( 12 a - 12\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-12{x}+12a-12$ |
| 768.1-r1 |
768.1-r |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{8} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.577633854$ |
$7.582692143$ |
3.989688880 |
\( -\frac{14336}{9} a - \frac{26624}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -20 a - 45\) , \( -90 a - 222\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-20a-45\right){x}-90a-222$ |
| 768.1-r2 |
768.1-r |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.288816927$ |
$7.582692143$ |
3.989688880 |
\( \frac{35168288}{3} a + \frac{86153392}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 254 a - 622\) , \( -2336 a + 5722\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(254a-622\right){x}-2336a+5722$ |
| 768.1-s1 |
768.1-s |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.424185996$ |
$6.405092923$ |
4.436761957 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 34 a + 84\) , \( -240 a - 588\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(34a+84\right){x}-240a-588$ |
| 768.1-s2 |
768.1-s |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.848371993$ |
$12.81018584$ |
4.436761957 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-3{x}-3$ |
| 768.1-t1 |
768.1-t |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{14} \cdot 3^{4} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.603762616$ |
$6.405092923$ |
3.157519378 |
\( \frac{4000}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 2\) , \( -2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+2{x}-2$ |
| 768.1-t2 |
768.1-t |
$2$ |
$2$ |
\(\Q(\sqrt{6}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{16} \cdot 3^{2} \) |
$2.30454$ |
$(-a+2), (a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.301881308$ |
$12.81018584$ |
3.157519378 |
\( \frac{16000}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 66 a - 161\) , \( 305 a - 747\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(66a-161\right){x}+305a-747$ |
*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.
