| 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 |
| 2.1-a1 |
2.1-a |
$2$ |
$5$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{5} \) |
$2.39048$ |
$(-a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$85.25278811$ |
0.715425505 |
\( \frac{4385}{8} a^{2} - \frac{4357}{8} a - \frac{7301}{2} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 3\) , \( 175273 a^{2} - 238953 a - 964825\) , \( -76487256 a^{2} + 104277237 a + 421036665\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(175273a^{2}-238953a-964825\right){x}-76487256a^{2}+104277237a+421036665$ |
| 2.1-a2 |
2.1-a |
$2$ |
$5$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( -2 \) |
$2.39048$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.682022304$ |
0.715425505 |
\( -\frac{3273665469537495}{2} a^{2} + \frac{9040027903531243}{2} a + 1858322751956986 \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 4\) , \( -1146 a^{2} + 3169 a + 1293\) , \( -40200 a^{2} + 111065 a + 45485\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-1146a^{2}+3169a+1293\right){x}-40200a^{2}+111065a+45485$ |
| 2.2-a1 |
2.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( -2 \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$155.1033639$ |
1.626998145 |
\( -\frac{345}{2} a^{2} + 100 a + 976 \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 4\) , \( -a\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}-a{x}-1$ |
| 2.2-a2 |
2.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{4} \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$155.1033639$ |
1.626998145 |
\( \frac{103522211}{16} a^{2} - \frac{35750543}{2} a - \frac{58561629}{8} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - a - 3\) , \( 37 a^{2} - 41 a - 235\) , \( -193 a^{2} + 283 a + 999\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(37a^{2}-41a-235\right){x}-193a^{2}+283a+999$ |
| 2.2-a3 |
2.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( - 2^{2} \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$19.38792049$ |
1.626998145 |
\( \frac{1146073068077217}{4} a^{2} - 791236577984564 a - \frac{650602251156401}{2} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - a - 3\) , \( -128 a^{2} + 329 a + 220\) , \( -2007 a^{2} + 4283 a + 6213\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-128a^{2}+329a+220\right){x}-2007a^{2}+4283a+6213$ |
| 2.2-a4 |
2.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2 \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$155.1033639$ |
1.626998145 |
\( \frac{98286043153}{2} a^{2} + 104426897384 a + 31459050232 \) |
\( \bigl[1\) , \( a^{2} - 3 a - 3\) , \( a^{2} - 2 a - 4\) , \( 17 a^{2} - 24 a - 90\) , \( 50 a^{2} - 68 a - 275\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(17a^{2}-24a-90\right){x}+50a^{2}-68a-275$ |
| 2.2-a5 |
2.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{2} \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$310.2067278$ |
1.626998145 |
\( \frac{216775}{4} a^{2} + 112050 a + \frac{73281}{2} \) |
\( \bigl[1\) , \( a^{2} - 3 a - 3\) , \( a^{2} - 2 a - 4\) , \( 2 a^{2} - 4 a - 5\) , \( a^{2} - 2 a - 4\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(2a^{2}-4a-5\right){x}+a^{2}-2a-4$ |
| 2.2-a6 |
2.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{8} \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$77.55168197$ |
1.626998145 |
\( -\frac{40396781037}{256} a^{2} + \frac{6884308025}{32} a + \frac{111184945547}{128} \) |
\( \bigl[1\) , \( 1\) , \( a^{2} - 2 a - 4\) , \( 4324 a^{2} - 5867 a - 23889\) , \( -241699 a^{2} + 329668 a + 1329994\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+{x}^{2}+\left(4324a^{2}-5867a-23889\right){x}-241699a^{2}+329668a+1329994$ |
| 2.2-b1 |
2.2-b |
$4$ |
$10$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2 \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$2.001264019$ |
0.524819830 |
\( \frac{1996462243425597306267}{2} a^{2} + 2121126756084321137476 a + 638891343281505678867 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 2 a - 3\) , \( 820505344 a^{2} - 1118618106 a - 4516606516\) , \( 19977278279343 a^{2} - 27235587595267 a - 109968211626010\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(820505344a^{2}-1118618106a-4516606516\right){x}+19977278279343a^{2}-27235587595267a-109968211626010$ |
| 2.2-b2 |
2.2-b |
$4$ |
$10$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{2} \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2 \) |
$1$ |
$1.000632009$ |
0.524819830 |
\( -\frac{3898289078247712509}{4} a^{2} + 1328661868305487506 a + \frac{10729386370458357755}{2} \) |
\( \bigl[a\) , \( a\) , \( 1\) , \( 14298089 a^{2} - 19492987 a - 78706177\) , \( 45955858568 a^{2} - 62652919683 a - 252971576496\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(14298089a^{2}-19492987a-78706177\right){x}+45955858568a^{2}-62652919683a-252971576496$ |
| 2.2-b3 |
2.2-b |
$4$ |
$10$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{10} \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$125.0790012$ |
0.524819830 |
\( -\frac{6602589}{1024} a^{2} + \frac{2051241}{128} a + \frac{6600731}{512} \) |
\( \bigl[a\) , \( 1\) , \( a^{2} - a - 3\) , \( 2 a^{2} + 2 a\) , \( -50 a^{2} - 107 a - 34\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+{x}^{2}+\left(2a^{2}+2a\right){x}-50a^{2}-107a-34$ |
| 2.2-b4 |
2.2-b |
$4$ |
$10$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
2.2 |
\( 2 \) |
\( 2^{5} \) |
$2.39048$ |
$(a+1)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$250.1580024$ |
0.524819830 |
\( \frac{6098353787}{32} a^{2} - \frac{2105098191}{4} a - \frac{3461712973}{16} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 2 a - 3\) , \( 18 a^{2} - 27 a - 100\) , \( -41 a^{2} + 50 a + 212\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(18a^{2}-27a-100\right){x}-41a^{2}+50a+212$ |
| 4.1-a1 |
4.1-a |
$2$ |
$2$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( - 2^{8} \) |
$2.68322$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$146.9658692$ |
1.541637722 |
\( 85565 a^{2} + 180152 a + 54154 \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a - 1\) , \( a^{2} - 2 a - 4\) , \( -2 a^{2} + 8 a - 4\) , \( 5 a^{2} - 4 a - 36\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a^{2}+8a-4\right){x}+5a^{2}-4a-36$ |
| 4.1-a2 |
4.1-a |
$2$ |
$2$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{4} \) |
$2.68322$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$146.9658692$ |
1.541637722 |
\( -20333 a^{2} + 27336 a + 112518 \) |
\( \bigl[a\) , \( -a^{2} + a + 3\) , \( 0\) , \( 6 a^{2} - 17 a - 5\) , \( -12 a^{2} + 33 a + 14\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(6a^{2}-17a-5\right){x}-12a^{2}+33a+14$ |
| 8.1-a1 |
8.1-a |
$4$ |
$6$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{20} \) |
$3.01181$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$4.514752240$ |
0.852456581 |
\( \frac{179588131606155581}{4096} a^{2} + \frac{47700525298360567}{512} a + \frac{57470309292795077}{2048} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 3 a + 5\) , \( 0\) , \( 22892 a^{2} - 31208 a - 126010\) , \( 4046775 a^{2} - 5517082 a - 22276137\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(22892a^{2}-31208a-126010\right){x}+4046775a^{2}-5517082a-22276137$ |
| 8.1-a2 |
8.1-a |
$4$ |
$6$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{12} \) |
$3.01181$ |
$(-a), (a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$121.8983104$ |
0.852456581 |
\( \frac{2007261}{16} a^{2} - \frac{641065}{2} a - \frac{1055387}{8} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 3 a + 5\) , \( 0\) , \( -2223 a^{2} + 3032 a + 12240\) , \( -72186 a^{2} + 98414 a + 397361\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-2223a^{2}+3032a+12240\right){x}-72186a^{2}+98414a+397361$ |
| 8.1-a3 |
8.1-a |
$4$ |
$6$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{28} \) |
$3.01181$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$4.514752240$ |
0.852456581 |
\( -\frac{52371762795149}{16777216} a^{2} - \frac{2807415232743}{2097152} a + \frac{61477883004267}{8388608} \) |
\( \bigl[a\) , \( -a - 1\) , \( a^{2} - 2 a - 4\) , \( 438 a^{2} - 598 a - 2409\) , \( 7688 a^{2} - 10481 a - 42321\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(438a^{2}-598a-2409\right){x}+7688a^{2}-10481a-42321$ |
| 8.1-a4 |
8.1-a |
$4$ |
$6$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$3.01181$ |
$(-a), (a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$121.8983104$ |
0.852456581 |
\( -\frac{152269}{256} a^{2} + \frac{28249}{32} a + \frac{389931}{128} \) |
\( \bigl[a\) , \( -a - 1\) , \( a^{2} - 2 a - 4\) , \( 13 a^{2} - 18 a - 69\) , \( -24 a^{2} + 33 a + 131\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a^{2}-18a-69\right){x}-24a^{2}+33a+131$ |
| 8.2-a1 |
8.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{8} \) |
$3.01181$ |
$(-a)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.525148577$ |
$244.1467345$ |
1.008695812 |
\( 31765 a^{2} - 87048 a - 34118 \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -397487 a^{2} + 541908 a + 2188024\) , \( -26829897 a^{2} + 36577950 a + 147689597\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-397487a^{2}+541908a+2188024\right){x}-26829897a^{2}+36577950a+147689597$ |
| 8.2-a2 |
8.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$3.01181$ |
$(-a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.525148577$ |
$122.0733672$ |
1.008695812 |
\( -88753 a^{2} + 120656 a + 489666 \) |
\( \bigl[a\) , \( a^{2} - 3 a - 5\) , \( a^{2} - 2 a - 4\) , \( 46 a^{2} - 127 a - 50\) , \( 37 a^{2} - 102 a - 43\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(46a^{2}-127a-50\right){x}+37a^{2}-102a-43$ |
| 8.2-a3 |
8.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$3.01181$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$4.201188622$ |
$3.814792727$ |
1.008695812 |
\( 13695187967 a^{2} - 48415475842 a + 17560535152 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 286429 a^{2} - 389996 a - 1578265\) , \( 130581821 a^{2} - 178015895 a - 718840312\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(286429a^{2}-389996a-1578265\right){x}+130581821a^{2}-178015895a-718840312$ |
| 8.2-a4 |
8.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{8} \) |
$3.01181$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.100594311$ |
$30.51834181$ |
1.008695812 |
\( 17874943 a^{2} + 37847040 a + 11584266 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 17924 a^{2} - 24406 a - 98765\) , \( 2036757 a^{2} - 2776593 a - 11212214\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(17924a^{2}-24406a-98765\right){x}+2036757a^{2}-2776593a-11212214$ |
| 8.2-a5 |
8.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{10} \) |
$3.01181$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$4.201188622$ |
$3.814792727$ |
1.008695812 |
\( 5436116808761345 a^{2} + 11551125347074178 a + 3479242326376800 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 8299 a^{2} - 11296 a - 45745\) , \( 4212001 a^{2} - 5742059 a - 23186532\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(8299a^{2}-11296a-45745\right){x}+4212001a^{2}-5742059a-23186532$ |
| 8.2-a6 |
8.2-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( 2^{4} \) |
$3.01181$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.050297155$ |
$244.1467345$ |
1.008695812 |
\( 963 a^{2} + 2056 a + 2374 \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 1744 a^{2} - 2376 a - 9610\) , \( -7340 a^{2} + 10009 a + 40395\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1744a^{2}-2376a-9610\right){x}-7340a^{2}+10009a+40395$ |
| 8.3-a1 |
8.3-a |
$2$ |
$3$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{47} \) |
$3.01181$ |
$(-a), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$2.754842385$ |
1.040315568 |
\( \frac{3370076834809}{1048576} a^{2} - \frac{4594552460417}{1048576} a - \frac{1159439933125}{65536} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( 0\) , \( a^{2} - 2 a - 3\) , \( 4 a^{2} + 2 a - 6\) , \( -110 a^{2} - 254 a - 84\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(4a^{2}+2a-6\right){x}-110a^{2}-254a-84$ |
| 8.3-a2 |
8.3-a |
$2$ |
$3$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.3 |
\( 2^{3} \) |
\( - 2^{21} \) |
$3.01181$ |
$(-a), (a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$74.38074441$ |
1.040315568 |
\( -\frac{16899039}{128} a^{2} + \frac{46667515}{128} a + \frac{4796603}{32} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( 0\) , \( a^{2} - 2 a - 3\) , \( -a^{2} + 2 a - 1\) , \( 4 a^{2} + 10 a + 2\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{2}+2a-1\right){x}+4a^{2}+10a+2$ |
| 8.4-a1 |
8.4-a |
$2$ |
$2$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{11} \) |
$3.01181$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$228.1418180$ |
2.393154509 |
\( -152586 a^{2} + 208912 a + 845580 \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 3 a - 5\) , \( a + 1\) , \( 2 a^{2} - 4 a - 10\) , \( -3 a^{2} + 3 a + 15\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(2a^{2}-4a-10\right){x}-3a^{2}+3a+15$ |
| 8.4-a2 |
8.4-a |
$2$ |
$2$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
8.4 |
\( 2^{3} \) |
\( 2^{10} \) |
$3.01181$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$114.0709090$ |
2.393154509 |
\( -276 a^{2} + 288 a + 2008 \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + 3 a + 4\) , \( a + 1\) , \( -a^{2} + a + 13\) , \( -2 a^{2} + 4 a + 9\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(-a^{2}+a+13\right){x}-2a^{2}+4a+9$ |
| 10.1-a1 |
10.1-a |
$4$ |
$6$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2^{3} \cdot 5^{12} \) |
$3.12593$ |
$(a+1), (a^2-a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$2.624894544$ |
$6.454885401$ |
1.066393496 |
\( \frac{4888811360212501}{1953125000} a^{2} - \frac{1664768825342593}{244140625} a - \frac{3042926936371107}{976562500} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} - 2 a - 3\) , \( 12253 a^{2} - 16704 a - 67452\) , \( 1157870 a^{2} - 1578552 a - 6373701\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}-a{x}^{2}+\left(12253a^{2}-16704a-67452\right){x}+1157870a^{2}-1578552a-6373701$ |
| 10.1-a2 |
10.1-a |
$4$ |
$6$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5^{4} \) |
$3.12593$ |
$(a+1), (a^2-a-7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.874964848$ |
$174.2819058$ |
1.066393496 |
\( \frac{14027589}{1250} a^{2} + \frac{14136892}{625} a + \frac{4486477}{625} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} - 2 a - 3\) , \( -317 a^{2} + 431 a + 1748\) , \( 8176 a^{2} - 11146 a - 45008\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}-a{x}^{2}+\left(-317a^{2}+431a+1748\right){x}+8176a^{2}-11146a-45008$ |
| 10.1-a3 |
10.1-a |
$4$ |
$6$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{6} \cdot 5^{6} \) |
$3.12593$ |
$(a+1), (a^2-a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1.312447272$ |
$6.454885401$ |
1.066393496 |
\( -\frac{19548678977671109}{1000000} a^{2} + \frac{3331408345633137}{125000} a + \frac{53804457088610163}{500000} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 3\) , \( 213 a^{2} - 291 a - 1175\) , \( 2810 a^{2} - 3831 a - 15471\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(213a^{2}-291a-1175\right){x}+2810a^{2}-3831a-15471$ |
| 10.1-a4 |
10.1-a |
$4$ |
$6$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
10.1 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$3.12593$ |
$(a+1), (a^2-a-7)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.437482424$ |
$174.2819058$ |
1.066393496 |
\( -\frac{89941}{100} a^{2} + \frac{23426}{25} a + \frac{290787}{50} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 3\) , \( 3 a^{2} - 6 a - 15\) , \( 5 a^{2} - 7 a - 30\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(3a^{2}-6a-15\right){x}+5a^{2}-7a-30$ |
| 10.2-a1 |
10.2-a |
$4$ |
$4$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( - 2 \cdot 5 \) |
$3.12593$ |
$(-a), (a^2-a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.146333803$ |
$43.24902882$ |
1.560179453 |
\( -\frac{185016154757}{10} a^{2} + \frac{252237752583}{10} a + \frac{509225920264}{5} \) |
\( \bigl[a^{2} - a - 3\) , \( a^{2} - 2 a - 3\) , \( a\) , \( 369 a^{2} - 505 a - 2026\) , \( 5924 a^{2} - 8077 a - 32608\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(369a^{2}-505a-2026\right){x}+5924a^{2}-8077a-32608$ |
| 10.2-a2 |
10.2-a |
$4$ |
$4$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{4} \cdot 5 \) |
$3.12593$ |
$(-a), (a^2-a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.286583450$ |
$86.49805764$ |
1.560179453 |
\( \frac{16089}{20} a^{2} - \frac{10969}{5} a - \frac{20001}{20} \) |
\( \bigl[a^{2} - a - 3\) , \( -a - 1\) , \( a\) , \( -2 a - 1\) , \( -11 a^{2} - 23 a - 7\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a-1\right){x}-11a^{2}-23a-7$ |
| 10.2-a3 |
10.2-a |
$4$ |
$4$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2 \cdot 5^{4} \) |
$3.12593$ |
$(-a), (a^2-a-7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.146333803$ |
$21.62451441$ |
1.560179453 |
\( \frac{291332027161}{1250} a^{2} + \frac{496370240341}{1250} a + \frac{70944749648}{625} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 4\) , \( 3 a^{2} - 9 a - 26\) , \( 4 a^{2} - 11 a - 32\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(3a^{2}-9a-26\right){x}+4a^{2}-11a-32$ |
| 10.2-a4 |
10.2-a |
$4$ |
$4$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
10.2 |
\( 2 \cdot 5 \) |
\( 2^{2} \cdot 5^{2} \) |
$3.12593$ |
$(-a), (a^2-a-7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.573166901$ |
$86.49805764$ |
1.560179453 |
\( -\frac{2816931}{50} a^{2} + \frac{2168457}{25} a + \frac{17004659}{50} \) |
\( \bigl[1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 4\) , \( 3 a^{2} - 4 a - 16\) , \( 10 a^{2} - 14 a - 56\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(3a^{2}-4a-16\right){x}+10a^{2}-14a-56$ |
| 16.1-a1 |
16.1-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{10} \) |
$3.38064$ |
$(-a), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$123.3182865$ |
2.587160180 |
\( \frac{115255893}{4} a^{2} - 79551362 a - \frac{65418851}{2} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 3 a + 3\) , \( a^{2} - 2 a - 4\) , \( 1811605 a^{2} - 2469812 a - 9972276\) , \( 2695517231 a^{2} - 3674874756 a - 14837917618\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+3a+3\right){x}^{2}+\left(1811605a^{2}-2469812a-9972276\right){x}+2695517231a^{2}-3674874756a-14837917618$ |
| 16.1-a2 |
16.1-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$3.38064$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$15.41478581$ |
2.587160180 |
\( -\frac{85551331344485}{4} a^{2} + 29158636453938 a + \frac{235465682028075}{2} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( 545990 a^{2} - 744363 a - 3005489\) , \( 342306517 a^{2} - 466676140 a - 1884282481\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(545990a^{2}-744363a-3005489\right){x}+342306517a^{2}-466676140a-1884282481$ |
| 16.1-a3 |
16.1-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$3.38064$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$123.3182865$ |
2.587160180 |
\( -\frac{33471037}{16} a^{2} + \frac{5698825}{2} a + \frac{92205243}{8} \) |
\( \bigl[a\) , \( a^{2} - a - 4\) , \( a^{2} - a - 4\) , \( 34125 a^{2} - 46523 a - 187844\) , \( 5318658 a^{2} - 7251076 a - 29277426\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(34125a^{2}-46523a-187844\right){x}+5318658a^{2}-7251076a-29277426$ |
| 16.1-a4 |
16.1-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{26} \) |
$3.38064$ |
$(-a), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$30.82957163$ |
2.587160180 |
\( -\frac{246018605}{65536} a^{2} + \frac{39985209}{8192} a + \frac{680916171}{32768} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 23 a^{2} - 32 a - 129\) , \( -100 a^{2} + 136 a + 549\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(23a^{2}-32a-129\right){x}-100a^{2}+136a+549$ |
| 16.1-a5 |
16.1-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{14} \) |
$3.38064$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$7.707392908$ |
2.587160180 |
\( \frac{2087488848157}{16} a^{2} + \frac{554437574607}{2} a + \frac{667989316853}{8} \) |
\( \bigl[a\) , \( -a^{2} + 3 a + 5\) , \( a^{2} - 2 a - 4\) , \( -73 a^{2} - 149 a - 32\) , \( -1140 a^{2} - 2422 a - 731\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-73a^{2}-149a-32\right){x}-1140a^{2}-2422a-731$ |
| 16.1-a6 |
16.1-a |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$3.38064$ |
$(-a), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$61.65914326$ |
2.587160180 |
\( \frac{22374003}{256} a^{2} + \frac{5926937}{32} a + \frac{7649387}{128} \) |
\( \bigl[a\) , \( -a^{2} + 3 a + 5\) , \( a^{2} - 2 a - 4\) , \( -3 a^{2} - 9 a - 2\) , \( -24 a^{2} - 54 a - 23\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-3a^{2}-9a-2\right){x}-24a^{2}-54a-23$ |
| 16.2-a1 |
16.2-a |
$2$ |
$2$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$3.38064$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.425141448$ |
$75.24698793$ |
2.013444483 |
\( 85565 a^{2} + 180152 a + 54154 \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 3 a + 4\) , \( a^{2} - 2 a - 4\) , \( -a^{2} + 2 a + 5\) , \( -a^{2} + a + 3\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+3a+4\right){x}^{2}+\left(-a^{2}+2a+5\right){x}-a^{2}+a+3$ |
| 16.2-a2 |
16.2-a |
$2$ |
$2$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$3.38064$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$0.850282897$ |
$75.24698793$ |
2.013444483 |
\( -20333 a^{2} + 27336 a + 112518 \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 5\) , \( a\) , \( -2 a^{2} + 6\) , \( -4 a^{2} - 6 a + 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-2a^{2}+6\right){x}-4a^{2}-6a+1$ |
| 16.2-b1 |
16.2-b |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{8} \) |
$3.38064$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$97.02914813$ |
1.017813154 |
\( 31765 a^{2} - 87048 a - 34118 \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 3 a + 5\) , \( a^{2} - 2 a - 4\) , \( -2 a^{2} + 4 a + 10\) , \( -2 a^{2} + 2 a + 8\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-2a^{2}+4a+10\right){x}-2a^{2}+2a+8$ |
| 16.2-b2 |
16.2-b |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$3.38064$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$48.51457406$ |
1.017813154 |
\( 13695187967 a^{2} - 48415475842 a + 17560535152 \) |
\( \bigl[a\) , \( a^{2} - 3 a - 5\) , \( a\) , \( 10267 a^{2} - 13986 a - 56555\) , \( 872750 a^{2} - 1189867 a - 4804129\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(10267a^{2}-13986a-56555\right){x}+872750a^{2}-1189867a-4804129$ |
| 16.2-b3 |
16.2-b |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$3.38064$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$194.0582962$ |
1.017813154 |
\( 17874943 a^{2} + 37847040 a + 11584266 \) |
\( \bigl[a\) , \( a^{2} - 3 a - 5\) , \( a\) , \( 642 a^{2} - 876 a - 3535\) , \( 12998 a^{2} - 17721 a - 71551\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(642a^{2}-876a-3535\right){x}+12998a^{2}-17721a-71551$ |
| 16.2-b4 |
16.2-b |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{10} \) |
$3.38064$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$48.51457406$ |
1.017813154 |
\( 5436116808761345 a^{2} + 11551125347074178 a + 3479242326376800 \) |
\( \bigl[a\) , \( a^{2} - 3 a - 5\) , \( a\) , \( 297 a^{2} - 406 a - 1635\) , \( 28194 a^{2} - 38439 a - 155197\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(297a^{2}-406a-1635\right){x}+28194a^{2}-38439a-155197$ |
| 16.2-b5 |
16.2-b |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{4} \) |
$3.38064$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$388.1165925$ |
1.017813154 |
\( 963 a^{2} + 2056 a + 2374 \) |
\( \bigl[a\) , \( a^{2} - 3 a - 5\) , \( a\) , \( 62 a^{2} - 86 a - 340\) , \( -129 a^{2} + 175 a + 710\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(62a^{2}-86a-340\right){x}-129a^{2}+175a+710$ |
| 16.2-b6 |
16.2-b |
$6$ |
$8$ |
3.3.568.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( 2^{8} \) |
$3.38064$ |
$(-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$194.0582962$ |
1.017813154 |
\( -88753 a^{2} + 120656 a + 489666 \) |
\( \bigl[a\) , \( a^{2} - a - 3\) , \( a^{2} - 2 a - 4\) , \( 4453 a^{2} - 6070 a - 24502\) , \( -255606 a^{2} + 348476 a + 1407030\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(4453a^{2}-6070a-24502\right){x}-255606a^{2}+348476a+1407030$ |
*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.
