| 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 |
| 1.1-a1 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$64$ |
\( 1 \) |
$1$ |
$5.419512290$ |
1.020143490 |
\( \frac{683335046841689195525}{3} a^{3} + 724241031993443727360 a^{2} - \frac{608323835837692722475}{3} a - 644739479834311245080 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - \frac{3}{2}\) , \( \frac{1}{6} a^{3} - \frac{1}{2} a^{2} - \frac{11}{6} a + 2\) , \( a\) , \( -\frac{14}{3} a^{3} - \frac{5}{2} a^{2} + \frac{257}{6} a + \frac{3}{2}\) , \( -\frac{11}{6} a^{3} + \frac{19}{2} a^{2} + \frac{25}{6} a - 157\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{3}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{2}a^{2}-\frac{11}{6}a+2\right){x}^{2}+\left(-\frac{14}{3}a^{3}-\frac{5}{2}a^{2}+\frac{257}{6}a+\frac{3}{2}\right){x}-\frac{11}{6}a^{3}+\frac{19}{2}a^{2}+\frac{25}{6}a-157$ |
| 1.1-a2 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$64$ |
\( 1 \) |
$1$ |
$5.419512290$ |
1.020143490 |
\( -\frac{683335046841689195525}{3} a^{3} + 724241031993443727360 a^{2} + \frac{608323835837692722475}{3} a - 644739479834311245080 \) |
\( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - \frac{3}{2}\) , \( -\frac{1}{6} a^{3} - \frac{1}{2} a^{2} + \frac{11}{6} a + 2\) , \( a\) , \( \frac{25}{6} a^{3} - 2 a^{2} - \frac{124}{3} a + \frac{3}{2}\) , \( \frac{11}{6} a^{3} + \frac{19}{2} a^{2} - \frac{25}{6} a - 157\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{3}{2}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{1}{2}a^{2}+\frac{11}{6}a+2\right){x}^{2}+\left(\frac{25}{6}a^{3}-2a^{2}-\frac{124}{3}a+\frac{3}{2}\right){x}+\frac{11}{6}a^{3}+\frac{19}{2}a^{2}-\frac{25}{6}a-157$ |
| 1.1-a3 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$16$ |
\( 1 \) |
$1$ |
$86.71219665$ |
1.020143490 |
\( 12534349815 a^{2} - 11158420645 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - \frac{3}{2}\) , \( \frac{1}{6} a^{3} - \frac{1}{2} a^{2} - \frac{11}{6} a + 2\) , \( a\) , \( \frac{7}{6} a^{3} - \frac{34}{3} a - \frac{17}{2}\) , \( \frac{3}{2} a^{3} + \frac{1}{2} a^{2} - \frac{27}{2} a - 15\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{3}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{2}a^{2}-\frac{11}{6}a+2\right){x}^{2}+\left(\frac{7}{6}a^{3}-\frac{34}{3}a-\frac{17}{2}\right){x}+\frac{3}{2}a^{3}+\frac{1}{2}a^{2}-\frac{27}{2}a-15$ |
| 1.1-a4 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1387.395146$ |
1.020143490 |
\( \frac{6107725}{3} a^{3} + 6473610 a^{2} - \frac{5434325}{3} a - 5762180 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a - \frac{1}{2}\) , \( a - 1\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 3\) , \( \frac{13}{2} a^{3} + \frac{13}{2} a^{2} - \frac{133}{2} a - 62\) , \( \frac{17}{6} a^{3} + \frac{5}{2} a^{2} - \frac{169}{6} a - 27\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-3\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(\frac{13}{2}a^{3}+\frac{13}{2}a^{2}-\frac{133}{2}a-62\right){x}+\frac{17}{6}a^{3}+\frac{5}{2}a^{2}-\frac{169}{6}a-27$ |
| 1.1-a5 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1387.395146$ |
1.020143490 |
\( -\frac{6107725}{3} a^{3} + 6473610 a^{2} + \frac{5434325}{3} a - 5762180 \) |
\( \bigl[1\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{17}{6} a - 3\) , \( -\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{11}{6} a - 1\) , \( -\frac{4}{3} a^{3} + a^{2} + \frac{35}{3} a - 6\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - \frac{11}{2}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{11}{6}a-1\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{17}{6}a-3\right){x}^{2}+\left(-\frac{4}{3}a^{3}+a^{2}+\frac{35}{3}a-6\right){x}+\frac{1}{2}a^{2}-\frac{3}{2}a-\frac{11}{2}$ |
| 1.1-a6 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$4$ |
\( 1 \) |
$1$ |
$1387.395146$ |
1.020143490 |
\( 35685 a^{2} - 20080 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - \frac{3}{2}\) , \( \frac{1}{6} a^{3} - \frac{1}{2} a^{2} - \frac{11}{6} a + 2\) , \( a\) , \( \frac{1}{3} a^{3} - \frac{14}{3} a - 1\) , \( -\frac{1}{6} a^{3} - \frac{1}{2} a^{2} + \frac{11}{6} a + 3\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{3}{2}\right){x}{y}+a{y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{2}a^{2}-\frac{11}{6}a+2\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{14}{3}a-1\right){x}-\frac{1}{6}a^{3}-\frac{1}{2}a^{2}+\frac{11}{6}a+3$ |
| 1.1-a7 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$4$ |
\( 1 \) |
$1$ |
$1387.395146$ |
1.020143490 |
\( -35685 a^{2} + 372455 \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( -\frac{1}{6} a^{3} + \frac{4}{3} a - \frac{1}{2}\) , \( a + 1\) , \( -\frac{2}{3} a^{3} - \frac{1}{2} a^{2} + \frac{23}{6} a + \frac{7}{2}\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{4}{3}a-\frac{1}{2}\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{1}{2}a^{2}+\frac{23}{6}a+\frac{7}{2}\right){x}$ |
| 1.1-a8 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1387.395146$ |
1.020143490 |
\( \frac{20583550}{3} a^{3} - 6473610 a^{2} - \frac{208095875}{3} a + 65447530 \) |
\( \bigl[1\) , \( -\frac{1}{6} a^{3} - \frac{1}{2} a^{2} + \frac{17}{6} a + 4\) , \( -\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{11}{6} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{13}{2} a + 9\) , \( -\frac{7}{6} a^{3} + \frac{22}{3} a + \frac{7}{2}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{11}{6}a-2\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{1}{2}a^{2}+\frac{17}{6}a+4\right){x}^{2}+\left(-\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+\frac{13}{2}a+9\right){x}-\frac{7}{6}a^{3}+\frac{22}{3}a+\frac{7}{2}$ |
| 1.1-a9 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$1387.395146$ |
1.020143490 |
\( -\frac{20583550}{3} a^{3} - 6473610 a^{2} + \frac{208095875}{3} a + 65447530 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{2}\) , \( -\frac{1}{3} a^{3} + \frac{11}{3} a + 2\) , \( -\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{11}{6} a - 1\) , \( -\frac{7}{3} a^{3} - \frac{13}{2} a^{2} + \frac{37}{6} a + \frac{23}{2}\) , \( -3 a^{3} - 9 a^{2} + 6 a + 10\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{2}\right){x}{y}+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{11}{6}a-1\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{11}{3}a+2\right){x}^{2}+\left(-\frac{7}{3}a^{3}-\frac{13}{2}a^{2}+\frac{37}{6}a+\frac{23}{2}\right){x}-3a^{3}-9a^{2}+6a+10$ |
| 1.1-a10 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2Cs, 3B |
$16$ |
\( 1 \) |
$1$ |
$86.71219665$ |
1.020143490 |
\( -12534349815 a^{2} + 126719427320 \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( -\frac{1}{6} a^{3} + \frac{4}{3} a - \frac{1}{2}\) , \( a + 1\) , \( -\frac{3}{2} a^{3} - \frac{1}{2} a^{2} + \frac{21}{2} a - 4\) , \( -a^{3} - a^{2} + 6 a - 7\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{4}{3}a-\frac{1}{2}\right){x}^{2}+\left(-\frac{3}{2}a^{3}-\frac{1}{2}a^{2}+\frac{21}{2}a-4\right){x}-a^{3}-a^{2}+6a-7$ |
| 1.1-a11 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$64$ |
\( 1 \) |
$1$ |
$5.419512290$ |
1.020143490 |
\( \frac{2302787226473629476100}{3} a^{3} - 724241031993443727360 a^{2} - \frac{23280654350684856650525}{3} a + 7321911872093569755880 \) |
\( \bigl[-\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{11}{6} a - 2\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a - \frac{1}{2}\) , \( a + 1\) , \( -\frac{7}{3} a^{3} + 2 a^{2} + \frac{32}{3} a - 23\) , \( -\frac{16}{3} a^{3} - 10 a^{2} + \frac{158}{3} a - 50\bigr] \) |
${y}^2+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{11}{6}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{4}{3}a-\frac{1}{2}\right){x}^{2}+\left(-\frac{7}{3}a^{3}+2a^{2}+\frac{32}{3}a-23\right){x}-\frac{16}{3}a^{3}-10a^{2}+\frac{158}{3}a-50$ |
| 1.1-a12 |
1.1-a |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.59552$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
✓ |
$2, 3$ |
2B, 3B |
$64$ |
\( 1 \) |
$1$ |
$5.419512290$ |
1.020143490 |
\( -\frac{2302787226473629476100}{3} a^{3} - 724241031993443727360 a^{2} + \frac{23280654350684856650525}{3} a + 7321911872093569755880 \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( -\frac{1}{6} a^{3} + \frac{4}{3} a - \frac{1}{2}\) , \( a + 1\) , \( \frac{11}{6} a^{3} + 2 a^{2} - \frac{26}{3} a - \frac{43}{2}\) , \( \frac{16}{3} a^{3} - 10 a^{2} - \frac{161}{3} a - 50\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{4}{3}a-\frac{1}{2}\right){x}^{2}+\left(\frac{11}{6}a^{3}+2a^{2}-\frac{26}{3}a-\frac{43}{2}\right){x}+\frac{16}{3}a^{3}-10a^{2}-\frac{161}{3}a-50$ |
| 4.1-a1 |
4.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$9.03265$ |
$(-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$140.2156679$ |
1.649596093 |
\( \frac{818888953}{24} a^{3} + \frac{515058159}{16} a^{2} - \frac{16557288871}{48} a - \frac{5207405429}{16} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 3\) , \( -\frac{1}{3} a^{3} + \frac{1}{2} a^{2} + \frac{19}{6} a - \frac{5}{2}\) , \( 1\) , \( \frac{11}{3} a^{3} + \frac{7}{2} a^{2} - \frac{227}{6} a - \frac{63}{2}\) , \( \frac{59}{3} a^{3} + 19 a^{2} - \frac{598}{3} a - 190\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-3\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{2}a^{2}+\frac{19}{6}a-\frac{5}{2}\right){x}^{2}+\left(\frac{11}{3}a^{3}+\frac{7}{2}a^{2}-\frac{227}{6}a-\frac{63}{2}\right){x}+\frac{59}{3}a^{3}+19a^{2}-\frac{598}{3}a-190$ |
| 4.1-a2 |
4.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{18} \) |
$9.03265$ |
$(-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$140.2156679$ |
1.649596093 |
\( \frac{218155}{3072} a^{3} - \frac{1527085}{1536} a + \frac{590557}{1024} \) |
\( \bigl[\frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 3\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a - \frac{3}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( \frac{11}{3} a^{3} - \frac{5}{2} a^{2} - \frac{227}{6} a + \frac{57}{2}\) , \( \frac{31}{6} a^{3} - \frac{9}{2} a^{2} - \frac{323}{6} a + 48\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-3\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{3}a-\frac{3}{2}\right){x}^{2}+\left(\frac{11}{3}a^{3}-\frac{5}{2}a^{2}-\frac{227}{6}a+\frac{57}{2}\right){x}+\frac{31}{6}a^{3}-\frac{9}{2}a^{2}-\frac{323}{6}a+48$ |
| 4.1-a3 |
4.1-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.1 |
\( 2^{2} \) |
\( 2^{6} \) |
$9.03265$ |
$(-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$140.2156679$ |
1.649596093 |
\( -\frac{486089365}{48} a^{3} - \frac{515058159}{16} a^{2} + \frac{433649297}{48} a + 28639645 \) |
\( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( \frac{1}{6} a^{3} - \frac{1}{2} a^{2} - \frac{5}{6} a + 3\) , \( 1\) , \( -\frac{5}{6} a^{3} - 4 a^{2} - \frac{7}{3} a + \frac{19}{2}\) , \( -\frac{17}{3} a^{3} - 19 a^{2} + \frac{10}{3} a + 19\bigr] \) |
${y}^2+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{2}a^{2}-\frac{5}{6}a+3\right){x}^{2}+\left(-\frac{5}{6}a^{3}-4a^{2}-\frac{7}{3}a+\frac{19}{2}\right){x}-\frac{17}{3}a^{3}-19a^{2}+\frac{10}{3}a+19$ |
| 4.2-a1 |
4.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$9.03265$ |
$(1/6a^3-1/2a^2-5/6a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$140.2156679$ |
1.649596093 |
\( -\frac{818888953}{24} a^{3} + \frac{515058159}{16} a^{2} + \frac{16557288871}{48} a - \frac{5207405429}{16} \) |
\( \bigl[-\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{3}{2}\) , \( -\frac{1}{6} a^{3} - \frac{1}{2} a^{2} + \frac{17}{6} a + 3\) , \( 1\) , \( -\frac{2}{3} a^{3} + \frac{3}{2} a^{2} + \frac{35}{6} a - \frac{13}{2}\) , \( \frac{25}{6} a^{3} + 5 a^{2} - \frac{121}{3} a - \frac{105}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{3}{2}\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{1}{2}a^{2}+\frac{17}{6}a+3\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{3}{2}a^{2}+\frac{35}{6}a-\frac{13}{2}\right){x}+\frac{25}{6}a^{3}+5a^{2}-\frac{121}{3}a-\frac{105}{2}$ |
| 4.2-a2 |
4.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{18} \) |
$9.03265$ |
$(1/6a^3-1/2a^2-5/6a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Cs |
$1$ |
\( 1 \) |
$1$ |
$140.2156679$ |
1.649596093 |
\( -\frac{218155}{3072} a^{3} + \frac{1527085}{1536} a + \frac{590557}{1024} \) |
\( \bigl[-\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{11}{6} a - 1\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + \frac{7}{2}\) , \( 1\) , \( -3 a^{3} - 3 a^{2} + 33 a + 37\) , \( -\frac{49}{6} a^{3} - 7 a^{2} + \frac{259}{3} a + \frac{165}{2}\bigr] \) |
${y}^2+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{11}{6}a-1\right){x}{y}+{y}={x}^{3}+\left(-\frac{1}{2}a^{2}+\frac{1}{2}a+\frac{7}{2}\right){x}^{2}+\left(-3a^{3}-3a^{2}+33a+37\right){x}-\frac{49}{6}a^{3}-7a^{2}+\frac{259}{3}a+\frac{165}{2}$ |
| 4.2-a3 |
4.2-a |
$3$ |
$9$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{6} \) |
$9.03265$ |
$(1/6a^3-1/2a^2-5/6a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$140.2156679$ |
1.649596093 |
\( \frac{486089365}{48} a^{3} - \frac{515058159}{16} a^{2} - \frac{433649297}{48} a + 28639645 \) |
\( \bigl[-\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{3}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{17}{6} a - 4\) , \( 1\) , \( -\frac{1}{3} a^{3} - \frac{3}{2} a^{2} + \frac{1}{6} a + \frac{5}{2}\) , \( -\frac{1}{3} a^{3} - 4 a^{2} - \frac{1}{3} a + 3\bigr] \) |
${y}^2+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{3}{2}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{17}{6}a-4\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{3}{2}a^{2}+\frac{1}{6}a+\frac{5}{2}\right){x}-\frac{1}{3}a^{3}-4a^{2}-\frac{1}{3}a+3$ |
| 9.1-a1 |
9.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$9.99627$ |
$(-1/3a^3+11/3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$8.145025583$ |
$0.489243952$ |
1.687724263 |
\( \frac{732096671152080845}{81} a^{2} - \frac{72414754225154290}{9} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{3}{2}\) , \( 0\) , \( -434 a^{2} + 369\) , \( -11608 a^{2} + 10309\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{3}{2}\right){x}^{2}+\left(-434a^{2}+369\right){x}-11608a^{2}+10309$ |
| 9.1-a2 |
9.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{24} \) |
$9.99627$ |
$(-1/3a^3+11/3a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.715008527$ |
$39.62876016$ |
1.687724263 |
\( \frac{25207270205}{531441} a^{2} - \frac{2480055685}{59049} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{3}{2}\) , \( 0\) , \( -4 a^{2} + 4\) , \( -25 a^{2} + 22\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{3}{2}\right){x}^{2}+\left(-4a^{2}+4\right){x}-25a^{2}+22$ |
| 9.1-a3 |
9.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$9.99627$ |
$(-1/3a^3+11/3a)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.357504263$ |
$634.0601626$ |
1.687724263 |
\( -\frac{505895}{729} a^{2} + \frac{710440}{81} \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{3}{2}\) , \( 0\) , \( a^{2} - 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{3}{2}\right){x}^{2}+\left(a^{2}-1\right){x}$ |
| 9.1-a4 |
9.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$9.99627$ |
$(-1/3a^3+11/3a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.678752131$ |
$634.0601626$ |
1.687724263 |
\( \frac{84472975}{27} a^{3} - 2945345 a^{2} - \frac{94978750}{3} a + 29873410 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{2}\) , \( -\frac{1}{3} a^{3} + \frac{1}{2} a^{2} + \frac{19}{6} a - \frac{3}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{3}{2}\) , \( \frac{11}{3} a^{3} + \frac{11}{2} a^{2} - \frac{227}{6} a - \frac{101}{2}\) , \( -\frac{23}{2} a^{3} - 10 a^{2} + 117 a + \frac{199}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{2}a^{2}+\frac{19}{6}a-\frac{3}{2}\right){x}^{2}+\left(\frac{11}{3}a^{3}+\frac{11}{2}a^{2}-\frac{227}{6}a-\frac{101}{2}\right){x}-\frac{23}{2}a^{3}-10a^{2}+117a+\frac{199}{2}$ |
| 9.1-a5 |
9.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$9.99627$ |
$(-1/3a^3+11/3a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.678752131$ |
$634.0601626$ |
1.687724263 |
\( -\frac{84472975}{27} a^{3} - 2945345 a^{2} + \frac{94978750}{3} a + 29873410 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{2}\) , \( \frac{1}{3} a^{3} - \frac{1}{2} a^{2} - \frac{19}{6} a + \frac{5}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 3\) , \( \frac{13}{2} a^{3} + \frac{13}{2} a^{2} - \frac{133}{2} a - 64\) , \( 26 a^{3} + \frac{49}{2} a^{2} - \frac{525}{2} a - \frac{499}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{2}a^{2}-\frac{19}{6}a+\frac{5}{2}\right){x}^{2}+\left(\frac{13}{2}a^{3}+\frac{13}{2}a^{2}-\frac{133}{2}a-64\right){x}+26a^{3}+\frac{49}{2}a^{2}-\frac{525}{2}a-\frac{499}{2}$ |
| 9.1-a6 |
9.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$9.99627$ |
$(-1/3a^3+11/3a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2 \) |
$4.072512791$ |
$7.827903242$ |
1.687724263 |
\( -\frac{392415680105}{9} a^{2} + 441092350035 \) |
\( \bigl[a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{3}{2}\) , \( 0\) , \( -24 a^{2} + 4\) , \( -221 a^{2} + 172\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{3}{2}\right){x}^{2}+\left(-24a^{2}+4\right){x}-221a^{2}+172$ |
| 9.1-a7 |
9.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$9.99627$ |
$(-1/3a^3+11/3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$2.036256395$ |
$7.827903242$ |
1.687724263 |
\( \frac{27904956271310257372300}{3} a^{3} - 8776283842174223229380 a^{2} - \frac{282112751953285855094725}{3} a + 88726230658331470146865 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{2}\) , \( -\frac{1}{3} a^{3} + \frac{1}{2} a^{2} + \frac{19}{6} a - \frac{3}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{3}{2}\) , \( 12 a^{3} + 158 a^{2} - 122 a - 1593\) , \( \frac{1178}{3} a^{3} + \frac{4583}{2} a^{2} - \frac{23813}{6} a - \frac{46339}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{2}a^{2}+\frac{19}{6}a-\frac{3}{2}\right){x}^{2}+\left(12a^{3}+158a^{2}-122a-1593\right){x}+\frac{1178}{3}a^{3}+\frac{4583}{2}a^{2}-\frac{23813}{6}a-\frac{46339}{2}$ |
| 9.1-a8 |
9.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{2} \) |
$9.99627$ |
$(-1/3a^3+11/3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$2.036256395$ |
$7.827903242$ |
1.687724263 |
\( -\frac{27904956271310257372300}{3} a^{3} - 8776283842174223229380 a^{2} + \frac{282112751953285855094725}{3} a + 88726230658331470146865 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{2}\) , \( \frac{1}{3} a^{3} - \frac{1}{2} a^{2} - \frac{19}{6} a + \frac{5}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 3\) , \( \frac{3119}{6} a^{3} + 514 a^{2} - \frac{15767}{3} a - \frac{10393}{2}\) , \( \frac{117097}{6} a^{3} + \frac{37201}{2} a^{2} - \frac{1183823}{6} a - 188048\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-3\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{1}{2}a^{2}-\frac{19}{6}a+\frac{5}{2}\right){x}^{2}+\left(\frac{3119}{6}a^{3}+514a^{2}-\frac{15767}{3}a-\frac{10393}{2}\right){x}+\frac{117097}{6}a^{3}+\frac{37201}{2}a^{2}-\frac{1183823}{6}a-188048$ |
| 9.2-a1 |
9.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{2} \) |
$9.99627$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$2.036256395$ |
$7.827903242$ |
1.687724263 |
\( \frac{24841767031126976000575}{9} a^{3} + 8776283842174223229380 a^{2} - \frac{22114830900604419655625}{9} a - 7812891605584985376315 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a - \frac{1}{2}\) , \( -\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{5}{6} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( -\frac{925}{6} a^{3} - 514 a^{2} + \frac{409}{3} a + \frac{915}{2}\) , \( -\frac{17374}{3} a^{3} - \frac{37201}{2} a^{2} + \frac{30937}{6} a + \frac{33115}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{5}{6}a-3\right){x}^{2}+\left(-\frac{925}{6}a^{3}-514a^{2}+\frac{409}{3}a+\frac{915}{2}\right){x}-\frac{17374}{3}a^{3}-\frac{37201}{2}a^{2}+\frac{30937}{6}a+\frac{33115}{2}$ |
| 9.2-a2 |
9.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{2} \) |
$9.99627$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$2.036256395$ |
$7.827903242$ |
1.687724263 |
\( -\frac{24841767031126976000575}{9} a^{3} + 8776283842174223229380 a^{2} + \frac{22114830900604419655625}{9} a - 7812891605584985376315 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a - \frac{1}{2}\) , \( \frac{1}{6} a^{3} - \frac{1}{2} a^{2} - \frac{5}{6} a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( -\frac{11}{3} a^{3} - 157 a^{2} + \frac{7}{3} a + 139\) , \( -113 a^{3} - \frac{4269}{2} a^{2} + \frac{203}{2} a + \frac{3797}{2}\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{2}a^{2}-\frac{5}{6}a+1\right){x}^{2}+\left(-\frac{11}{3}a^{3}-157a^{2}+\frac{7}{3}a+139\right){x}-113a^{3}-\frac{4269}{2}a^{2}+\frac{203}{2}a+\frac{3797}{2}$ |
| 9.2-a3 |
9.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$9.99627$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$9$ |
\( 2 \) |
$4.072512791$ |
$7.827903242$ |
1.687724263 |
\( \frac{392415680105}{9} a^{2} - \frac{346741330840}{9} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - \frac{7}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( -a^{3} + \frac{53}{2} a^{2} + \frac{9}{2} a - \frac{543}{2}\) , \( -\frac{77}{6} a^{3} + 137 a^{2} + \frac{404}{3} a - \frac{2853}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-\frac{7}{2}\right){x}^{2}+\left(-a^{3}+\frac{53}{2}a^{2}+\frac{9}{2}a-\frac{543}{2}\right){x}-\frac{77}{6}a^{3}+137a^{2}+\frac{404}{3}a-\frac{2853}{2}$ |
| 9.2-a4 |
9.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$9.99627$ |
$(-a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.678752131$ |
$634.0601626$ |
1.687724263 |
\( \frac{74393975}{81} a^{3} + 2945345 a^{2} - \frac{58076950}{81} a - 2525385 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a - \frac{1}{2}\) , \( -\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{5}{6} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( -\frac{5}{3} a^{3} - \frac{13}{2} a^{2} - \frac{7}{6} a + \frac{15}{2}\) , \( -\frac{47}{6} a^{3} - \frac{49}{2} a^{2} + \frac{49}{6} a + 20\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{5}{6}a-3\right){x}^{2}+\left(-\frac{5}{3}a^{3}-\frac{13}{2}a^{2}-\frac{7}{6}a+\frac{15}{2}\right){x}-\frac{47}{6}a^{3}-\frac{49}{2}a^{2}+\frac{49}{6}a+20$ |
| 9.2-a5 |
9.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$9.99627$ |
$(-a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.678752131$ |
$634.0601626$ |
1.687724263 |
\( -\frac{74393975}{81} a^{3} + 2945345 a^{2} + \frac{58076950}{81} a - 2525385 \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a - \frac{1}{2}\) , \( \frac{1}{6} a^{3} - \frac{1}{2} a^{2} - \frac{5}{6} a + 1\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( -\frac{7}{6} a^{3} - \frac{9}{2} a^{2} - \frac{1}{6} a + 4\) , \( \frac{9}{2} a^{3} + \frac{29}{2} a^{2} - \frac{7}{2} a - 14\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{2}a^{2}-\frac{5}{6}a+1\right){x}^{2}+\left(-\frac{7}{6}a^{3}-\frac{9}{2}a^{2}-\frac{1}{6}a+4\right){x}+\frac{9}{2}a^{3}+\frac{29}{2}a^{2}-\frac{7}{2}a-14$ |
| 9.2-a6 |
9.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$9.99627$ |
$(-a)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.357504263$ |
$634.0601626$ |
1.687724263 |
\( \frac{505895}{729} a^{2} + \frac{829115}{729} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - \frac{7}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( -a^{3} + \frac{3}{2} a^{2} + \frac{9}{2} a - \frac{3}{2}\) , \( -\frac{1}{3} a^{3} + a^{2} - \frac{1}{3} a\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-\frac{7}{2}\right){x}^{2}+\left(-a^{3}+\frac{3}{2}a^{2}+\frac{9}{2}a-\frac{3}{2}\right){x}-\frac{1}{3}a^{3}+a^{2}-\frac{1}{3}a$ |
| 9.2-a7 |
9.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{24} \) |
$9.99627$ |
$(-a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.715008527$ |
$39.62876016$ |
1.687724263 |
\( -\frac{25207270205}{531441} a^{2} + \frac{254959471090}{531441} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - \frac{7}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( -a^{3} + \frac{13}{2} a^{2} + \frac{9}{2} a - \frac{103}{2}\) , \( -\frac{17}{6} a^{3} + 11 a^{2} + \frac{74}{3} a - \frac{201}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-\frac{7}{2}\right){x}^{2}+\left(-a^{3}+\frac{13}{2}a^{2}+\frac{9}{2}a-\frac{103}{2}\right){x}-\frac{17}{6}a^{3}+11a^{2}+\frac{74}{3}a-\frac{201}{2}$ |
| 9.2-a8 |
9.2-a |
$8$ |
$12$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$9.99627$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$8.145025583$ |
$0.489243952$ |
1.687724263 |
\( -\frac{732096671152080845}{81} a^{2} + \frac{7401330594646500685}{81} \) |
\( \bigl[a\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - \frac{7}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( -a^{3} + \frac{873}{2} a^{2} + \frac{9}{2} a - \frac{8833}{2}\) , \( -\frac{1307}{6} a^{3} + \frac{20543}{2} a^{2} + \frac{13243}{6} a - 103884\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){y}={x}^{3}+\left(\frac{1}{2}a^{2}-\frac{3}{2}a-\frac{7}{2}\right){x}^{2}+\left(-a^{3}+\frac{873}{2}a^{2}+\frac{9}{2}a-\frac{8833}{2}\right){x}-\frac{1307}{6}a^{3}+\frac{20543}{2}a^{2}+\frac{13243}{6}a-103884$ |
| 16.1-a1 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$200.9792493$ |
1.182230878 |
\( \frac{316763764621765253}{64} a^{3} + \frac{2014355762928143019}{128} a^{2} - \frac{563983800449091071}{128} a - \frac{1793235441544207553}{128} \) |
\( \bigl[a + 1\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{17}{6} a - 2\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 3\) , \( \frac{64}{3} a^{3} - \frac{45}{2} a^{2} - \frac{1237}{6} a + \frac{391}{2}\) , \( -\frac{697}{2} a^{3} + 333 a^{2} + 3508 a - \frac{6637}{2}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-3\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{17}{6}a-2\right){x}^{2}+\left(\frac{64}{3}a^{3}-\frac{45}{2}a^{2}-\frac{1237}{6}a+\frac{391}{2}\right){x}-\frac{697}{2}a^{3}+333a^{2}+3508a-\frac{6637}{2}$ |
| 16.1-a2 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$200.9792493$ |
1.182230878 |
\( -\frac{316763764621765253}{64} a^{3} + \frac{2014355762928143019}{128} a^{2} + \frac{563983800449091071}{128} a - \frac{1793235441544207553}{128} \) |
\( \bigl[a + 1\) , \( -\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{11}{6} a - 2\) , \( -\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{11}{6} a - 1\) , \( -\frac{131}{6} a^{3} - \frac{45}{2} a^{2} + \frac{1249}{6} a + 193\) , \( \frac{1046}{3} a^{3} + \frac{665}{2} a^{2} - \frac{21059}{6} a - \frac{6633}{2}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{11}{6}a-1\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{11}{6}a-2\right){x}^{2}+\left(-\frac{131}{6}a^{3}-\frac{45}{2}a^{2}+\frac{1249}{6}a+193\right){x}+\frac{1046}{3}a^{3}+\frac{665}{2}a^{2}-\frac{21059}{6}a-\frac{6633}{2}$ |
| 16.1-a3 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$200.9792493$ |
1.182230878 |
\( \frac{14052534045}{524288} a^{3} - \frac{98367738315}{262144} a + \frac{173673063889}{524288} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{2}\) , \( \frac{1}{6} a^{3} - \frac{1}{2} a^{2} - \frac{11}{6} a + 2\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - \frac{5}{2}\) , \( \frac{13}{3} a^{3} - \frac{41}{2} a^{2} + \frac{155}{6} a - \frac{25}{2}\) , \( -\frac{365}{6} a^{3} + \frac{417}{2} a^{2} - \frac{53}{6} a - 125\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a+\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}-\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{1}{2}a^{2}-\frac{11}{6}a+2\right){x}^{2}+\left(\frac{13}{3}a^{3}-\frac{41}{2}a^{2}+\frac{155}{6}a-\frac{25}{2}\right){x}-\frac{365}{6}a^{3}+\frac{417}{2}a^{2}-\frac{53}{6}a-125$ |
| 16.1-a4 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2 \) |
$1$ |
$200.9792493$ |
1.182230878 |
\( -\frac{14052534045}{524288} a^{3} + \frac{98367738315}{262144} a + \frac{173673063889}{524288} \) |
\( \bigl[\frac{1}{6} a^{3} - \frac{4}{3} a - \frac{1}{2}\) , \( -\frac{1}{6} a^{3} - \frac{1}{2} a^{2} + \frac{11}{6} a + 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - \frac{5}{2}\) , \( -\frac{25}{6} a^{3} - \frac{41}{2} a^{2} - \frac{169}{6} a - 13\) , \( \frac{365}{6} a^{3} + \frac{417}{2} a^{2} + \frac{53}{6} a - 125\bigr] \) |
${y}^2+\left(\frac{1}{6}a^{3}-\frac{4}{3}a-\frac{1}{2}\right){x}{y}+\left(\frac{1}{2}a^{2}+\frac{1}{2}a-\frac{5}{2}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}-\frac{1}{2}a^{2}+\frac{11}{6}a+2\right){x}^{2}+\left(-\frac{25}{6}a^{3}-\frac{41}{2}a^{2}-\frac{169}{6}a-13\right){x}+\frac{365}{6}a^{3}+\frac{417}{2}a^{2}+\frac{53}{6}a-125$ |
| 16.1-a5 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$200.9792493$ |
1.182230878 |
\( \frac{2134939673743248165}{128} a^{3} - \frac{2014355762928143019}{128} a^{2} - \frac{21583753823445138297}{128} a + \frac{2545584743833170707}{16} \) |
\( \bigl[a\) , \( -\frac{1}{6} a^{3} + \frac{1}{2} a^{2} + \frac{5}{6} a - 1\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{3}{2}\) , \( \frac{21}{2} a^{3} + 25 a^{2} - 54 a - \frac{135}{2}\) , \( -\frac{683}{6} a^{3} - \frac{651}{2} a^{2} + \frac{1531}{6} a + 438\bigr] \) |
${y}^2+a{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{1}{2}a^{2}+\frac{5}{6}a-1\right){x}^{2}+\left(\frac{21}{2}a^{3}+25a^{2}-54a-\frac{135}{2}\right){x}-\frac{683}{6}a^{3}-\frac{651}{2}a^{2}+\frac{1531}{6}a+438$ |
| 16.1-a6 |
16.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$200.9792493$ |
1.182230878 |
\( -\frac{2134939673743248165}{128} a^{3} - \frac{2014355762928143019}{128} a^{2} + \frac{21583753823445138297}{128} a + \frac{2545584743833170707}{16} \) |
\( \bigl[a\) , \( -\frac{1}{3} a^{3} + \frac{1}{2} a^{2} + \frac{19}{6} a - \frac{5}{2}\) , \( \frac{1}{6} a^{3} + \frac{1}{2} a^{2} - \frac{11}{6} a - 2\) , \( -\frac{65}{6} a^{3} + 24 a^{2} + \frac{152}{3} a - \frac{123}{2}\) , \( 118 a^{3} - \frac{643}{2} a^{2} - \frac{669}{2} a + \frac{1003}{2}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{6}a^{3}+\frac{1}{2}a^{2}-\frac{11}{6}a-2\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{1}{2}a^{2}+\frac{19}{6}a-\frac{5}{2}\right){x}^{2}+\left(-\frac{65}{6}a^{3}+24a^{2}+\frac{152}{3}a-\frac{123}{2}\right){x}+118a^{3}-\frac{643}{2}a^{2}-\frac{669}{2}a+\frac{1003}{2}$ |
| 16.1-b1 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$527.2239557$ |
1.378363283 |
\( \frac{110887}{1536} a^{3} - \frac{776209}{768} a + \frac{424577}{512} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a - \frac{5}{2}\) , \( -\frac{2}{3} a^{3} + \frac{28}{3} a + 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{3}a-\frac{5}{2}\right){x}-\frac{2}{3}a^{3}+\frac{28}{3}a+8$ |
| 16.1-b2 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$527.2239557$ |
1.378363283 |
\( -\frac{110887}{1536} a^{3} + \frac{776209}{768} a + \frac{424577}{512} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a - \frac{5}{2}\) , \( \frac{2}{3} a^{3} - \frac{28}{3} a + 8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a-\frac{5}{2}\right){x}+\frac{2}{3}a^{3}-\frac{28}{3}a+8$ |
| 16.1-b3 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$6.508937725$ |
1.378363283 |
\( \frac{55573026649}{100663296} a^{3} - \frac{389011186543}{50331648} a - \frac{227050752511}{33554432} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{3}{2} a^{3} - 21 a + \frac{35}{2}\) , \( -\frac{53}{3} a^{3} + \frac{742}{3} a - 219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(\frac{3}{2}a^{3}-21a+\frac{35}{2}\right){x}-\frac{53}{3}a^{3}+\frac{742}{3}a-219$ |
| 16.1-b4 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{54} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$6.508937725$ |
1.378363283 |
\( -\frac{55573026649}{100663296} a^{3} + \frac{389011186543}{50331648} a - \frac{227050752511}{33554432} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -\frac{3}{2} a^{3} + 21 a + \frac{35}{2}\) , \( \frac{53}{3} a^{3} - \frac{742}{3} a - 219\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-\frac{3}{2}a^{3}+21a+\frac{35}{2}\right){x}+\frac{53}{3}a^{3}-\frac{742}{3}a-219$ |
| 16.1-b5 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$6.508937725$ |
1.378363283 |
\( -\frac{653762688677050897}{384} a^{3} + \frac{4576338820739356279}{192} a + \frac{2695532619503868023}{128} \) |
\( \bigl[1\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a + \frac{1}{2}\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{1}{2}\) , \( \frac{491}{3} a^{3} - \frac{6874}{3} a - 2026\) , \( \frac{23629}{6} a^{3} - \frac{165403}{3} a - \frac{97427}{2}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{1}{2}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{3}a+\frac{1}{2}\right){x}^{2}+\left(\frac{491}{3}a^{3}-\frac{6874}{3}a-2026\right){x}+\frac{23629}{6}a^{3}-\frac{165403}{3}a-\frac{97427}{2}$ |
| 16.1-b6 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$26.03575090$ |
1.378363283 |
\( -\frac{67954182989}{8192} a^{3} + \frac{475679280923}{4096} a + \frac{840670387009}{8192} \) |
\( \bigl[1\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a + \frac{1}{2}\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{1}{2}\) , \( \frac{31}{3} a^{3} - \frac{434}{3} a - 126\) , \( \frac{349}{6} a^{3} - \frac{2443}{3} a - \frac{1443}{2}\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{1}{2}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{3}a+\frac{1}{2}\right){x}^{2}+\left(\frac{31}{3}a^{3}-\frac{434}{3}a-126\right){x}+\frac{349}{6}a^{3}-\frac{2443}{3}a-\frac{1443}{2}$ |
| 16.1-b7 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{6} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2 \) |
$1$ |
$527.2239557$ |
1.378363283 |
\( \frac{54503407609}{24} a^{3} - \frac{381523853263}{12} a + \frac{224726095901}{8} \) |
\( \bigl[1\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a + \frac{1}{2}\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{1}{2}\) , \( 2 a^{3} - 28 a - 26\) , \( \frac{14}{3} a^{3} - \frac{196}{3} a - 58\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{1}{2}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{3}a+\frac{1}{2}\right){x}^{2}+\left(2a^{3}-28a-26\right){x}+\frac{14}{3}a^{3}-\frac{196}{3}a-58$ |
| 16.1-b8 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2^{3} \) |
$1$ |
$2108.895823$ |
1.378363283 |
\( \frac{305319}{32} a^{3} - \frac{2137233}{16} a + \frac{3832069}{32} \) |
\( \bigl[1\) , \( \frac{1}{6} a^{3} - \frac{7}{3} a + \frac{1}{2}\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{1}{2}\) , \( \frac{1}{3} a^{3} - \frac{14}{3} a - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{1}{2}\right){y}={x}^{3}+\left(\frac{1}{6}a^{3}-\frac{7}{3}a+\frac{1}{2}\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{14}{3}a-1\right){x}$ |
| 16.1-b9 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$4$ |
\( 2 \cdot 3^{2} \) |
$1$ |
$6.508937725$ |
1.378363283 |
\( \frac{653762688677050897}{384} a^{3} - \frac{4576338820739356279}{192} a + \frac{2695532619503868023}{128} \) |
\( \bigl[1\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{1}{2}\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{3}{2}\) , \( -\frac{327}{2} a^{3} + 2289 a - \frac{4053}{2}\) , \( -3938 a^{3} + 55132 a - 48714\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{1}{2}\right){x}^{2}+\left(-\frac{327}{2}a^{3}+2289a-\frac{4053}{2}\right){x}-3938a^{3}+55132a-48714$ |
| 16.1-b10 |
16.1-b |
$12$ |
$24$ |
\(\Q(\sqrt{5}, \sqrt{17})\) |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$10.74169$ |
$(1/6a^3-1/2a^2-5/6a+2), (-1/6a^3-1/2a^2+5/6a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$26.03575090$ |
1.378363283 |
\( \frac{67954182989}{8192} a^{3} - \frac{475679280923}{4096} a + \frac{840670387009}{8192} \) |
\( \bigl[1\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{1}{2}\) , \( -\frac{1}{6} a^{3} + \frac{7}{3} a + \frac{3}{2}\) , \( -\frac{61}{6} a^{3} + \frac{427}{3} a - \frac{253}{2}\) , \( -58 a^{3} + 812 a - 722\bigr] \) |
${y}^2+{x}{y}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{3}{2}\right){y}={x}^{3}+\left(-\frac{1}{6}a^{3}+\frac{7}{3}a+\frac{1}{2}\right){x}^{2}+\left(-\frac{61}{6}a^{3}+\frac{427}{3}a-\frac{253}{2}\right){x}-58a^{3}+812a-722$ |
*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.
