| 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 |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$8.34682$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3, 5$ |
3Ns, 5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$88.09912591$ |
0.943167618 |
\( 8340 a^{3} - 16680 a^{2} - 41700 a + 17791 \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - \frac{4}{3} a + \frac{23}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{7}{3}\) , \( -3 a^{3} + 12 a^{2} + 15 a - 40\) , \( -12 a^{3} + 38 a^{2} + 71 a - 158\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{7}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-\frac{4}{3}a+\frac{23}{3}\right){x}^{2}+\left(-3a^{3}+12a^{2}+15a-40\right){x}-12a^{3}+38a^{2}+71a-158$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$10.98504$ |
$(2/3a^3-7/3a^2-7/3a+26/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$280.2331653$ |
1.500053742 |
\( -\frac{56524344650}{729} a^{3} - \frac{31164196204}{729} a^{2} + \frac{517337281243}{729} a + \frac{230409279685}{243} \) |
\( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( \frac{4}{3} a^{3} - \frac{8}{3} a^{2} - \frac{56}{3} a - \frac{47}{3}\) , \( -11 a^{3} - 16 a^{2} + 70 a + 110\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{22}{3}\right){x}^{2}+\left(\frac{4}{3}a^{3}-\frac{8}{3}a^{2}-\frac{56}{3}a-\frac{47}{3}\right){x}-11a^{3}-16a^{2}+70a+110$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$10.98504$ |
$(2/3a^3-7/3a^2-7/3a+26/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$560.4663307$ |
1.500053742 |
\( -\frac{44428}{27} a^{3} - \frac{55457}{27} a^{2} + \frac{420938}{27} a + \frac{255289}{9} \) |
\( \bigl[a^{2} - a - 4\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} - \frac{1}{3} a - \frac{7}{3}\) , \( -a^{3} + a^{2} + 4 a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{22}{3}\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}-\frac{1}{3}a-\frac{7}{3}\right){x}-a^{3}+a^{2}+4a-2$ |
| 9.2-a1 |
9.2-a |
$2$ |
$2$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{12} \) |
$10.98504$ |
$(-a^2+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$280.2331653$ |
1.500053742 |
\( -\frac{122498710823}{729} a^{3} + \frac{129736769050}{243} a^{2} + \frac{377777996122}{729} a - \frac{118723188188}{81} \) |
\( \bigl[a + 1\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{7}{3} a - \frac{23}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{140}{3} a^{3} + \frac{379}{3} a^{2} + \frac{760}{3} a - \frac{1574}{3}\) , \( -\frac{956}{3} a^{3} + \frac{2578}{3} a^{2} + \frac{5194}{3} a - \frac{10721}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{7}{3}a-\frac{23}{3}\right){x}^{2}+\left(-\frac{140}{3}a^{3}+\frac{379}{3}a^{2}+\frac{760}{3}a-\frac{1574}{3}\right){x}-\frac{956}{3}a^{3}+\frac{2578}{3}a^{2}+\frac{5194}{3}a-\frac{10721}{3}$ |
| 9.2-a2 |
9.2-a |
$2$ |
$2$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$10.98504$ |
$(-a^2+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$560.4663307$ |
1.500053742 |
\( -\frac{40825}{9} a^{3} + \frac{389263}{27} a^{2} + \frac{45953}{3} a - \frac{1079279}{27} \) |
\( \bigl[a + 1\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{7}{3} a - \frac{23}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{10}{3} a^{3} + \frac{29}{3} a^{2} + \frac{50}{3} a - \frac{109}{3}\) , \( -5 a^{3} + 14 a^{2} + 27 a - 57\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{7}{3}a-\frac{23}{3}\right){x}^{2}+\left(-\frac{10}{3}a^{3}+\frac{29}{3}a^{2}+\frac{50}{3}a-\frac{109}{3}\right){x}-5a^{3}+14a^{2}+27a-57$ |
| 11.1-a1 |
11.1-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{3} \) |
$11.26407$ |
$(a^2-a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.049747104$ |
$348.2097271$ |
2.225395646 |
\( -\frac{11621788}{3993} a^{3} + \frac{31432430}{3993} a^{2} + \frac{62552696}{3993} a - \frac{129634639}{3993} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{19}{3}\) , \( a^{2} - 6\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{19}{3}\) , \( a^{3} - 2 a^{2} - 4 a + 6\) , \( -\frac{26}{3} a^{3} - \frac{14}{3} a^{2} + \frac{250}{3} a + \frac{334}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{19}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{19}{3}\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(a^{3}-2a^{2}-4a+6\right){x}-\frac{26}{3}a^{3}-\frac{14}{3}a^{2}+\frac{250}{3}a+\frac{334}{3}$ |
| 11.2-a1 |
11.2-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{3} \) |
$11.26407$ |
$(2/3a^3-7/3a^2-7/3a+23/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.049747104$ |
$348.2097271$ |
2.225395646 |
\( -\frac{1951682}{3993} a^{3} - \frac{389590}{363} a^{2} + \frac{5314654}{3993} a + \frac{11755789}{3993} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{7}{3}\) , \( -a + 1\) , \( a + 1\) , \( -3 a^{3} + 8 a^{2} + 14 a - 31\) , \( \frac{124}{3} a^{3} - \frac{332}{3} a^{2} - \frac{686}{3} a + \frac{1399}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{7}{3}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a^{3}+8a^{2}+14a-31\right){x}+\frac{124}{3}a^{3}-\frac{332}{3}a^{2}-\frac{686}{3}a+\frac{1399}{3}$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$11.80419$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.016276665$ |
$1225.167218$ |
2.561883230 |
\( -\frac{105745}{24} a^{3} + \frac{143299}{12} a^{2} + \frac{45817}{3} a - \frac{340301}{12} \) |
\( \bigl[a^{2} - a - 5\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{16}{3}\) , \( a^{3} - 2 a^{2} - 8 a - 2\) , \( \frac{8}{3} a^{3} - \frac{1}{3} a^{2} - \frac{61}{3} a - \frac{61}{3}\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){x}^{2}+\left(a^{3}-2a^{2}-8a-2\right){x}+\frac{8}{3}a^{3}-\frac{1}{3}a^{2}-\frac{61}{3}a-\frac{61}{3}$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$11.80419$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.016276665$ |
$1225.167218$ |
2.561883230 |
\( -\frac{21175}{6} a^{3} + \frac{23573}{6} a^{2} + \frac{585689}{24} a + \frac{142685}{24} \) |
\( \bigl[a^{2} - a - 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{8}{3} a + \frac{7}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{19}{3}\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - \frac{1}{3} a - \frac{1}{3}\) , \( \frac{17}{3} a^{3} - \frac{52}{3} a^{2} - \frac{61}{3} a + \frac{152}{3}\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{19}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{8}{3}a+\frac{7}{3}\right){x}^{2}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-\frac{1}{3}a-\frac{1}{3}\right){x}+\frac{17}{3}a^{3}-\frac{52}{3}a^{2}-\frac{61}{3}a+\frac{152}{3}$ |
| 19.1-a1 |
19.1-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{2} \) |
$12.06050$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$48.01809018$ |
1.028139775 |
\( -\frac{245677148861}{1083} a^{3} - \frac{569100643382}{1083} a^{2} + \frac{573333572713}{1083} a + \frac{1410635319502}{1083} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -a^{2} + 4\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{19}{3}\) , \( \frac{1}{3} a^{3} - \frac{11}{3} a^{2} - \frac{2}{3} a + \frac{34}{3}\) , \( -\frac{1}{3} a^{3} - \frac{13}{3} a^{2} + \frac{5}{3} a + \frac{41}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{19}{3}\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{11}{3}a^{2}-\frac{2}{3}a+\frac{34}{3}\right){x}-\frac{1}{3}a^{3}-\frac{13}{3}a^{2}+\frac{5}{3}a+\frac{41}{3}$ |
| 19.1-a2 |
19.1-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{6} \) |
$12.06050$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$48.01809018$ |
1.028139775 |
\( -\frac{6006390739}{141137643} a^{3} - \frac{4672495858}{141137643} a^{2} + \frac{13480865687}{141137643} a + \frac{4689456125}{141137643} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{2}{3} a - \frac{1}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -\frac{4}{3} a^{3} - \frac{4}{3} a^{2} - \frac{1}{3} a + \frac{2}{3}\) , \( -\frac{7}{3} a^{3} - \frac{25}{3} a^{2} - \frac{37}{3} a - \frac{25}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{2}{3}a-\frac{1}{3}\right){x}^{2}+\left(-\frac{4}{3}a^{3}-\frac{4}{3}a^{2}-\frac{1}{3}a+\frac{2}{3}\right){x}-\frac{7}{3}a^{3}-\frac{25}{3}a^{2}-\frac{37}{3}a-\frac{25}{3}$ |
| 19.1-b1 |
19.1-b |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$12.06050$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.042884207$ |
$1265.568406$ |
2.324129283 |
\( -\frac{122515}{57} a^{3} + \frac{413975}{57} a^{2} + \frac{686690}{57} a - \frac{2076535}{57} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{2}{3} a - \frac{7}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{16}{3}\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{2}{3} a + \frac{2}{3}\) , \( \frac{4}{3} a^{3} + \frac{1}{3} a^{2} - \frac{11}{3} a - \frac{2}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{2}{3}a-\frac{7}{3}\right){x}^{2}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{2}{3}a+\frac{2}{3}\right){x}+\frac{4}{3}a^{3}+\frac{1}{3}a^{2}-\frac{11}{3}a-\frac{2}{3}$ |
| 19.1-c1 |
19.1-c |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$12.06050$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.016349061$ |
$1185.630756$ |
2.490237769 |
\( \frac{15350903}{20577} a^{3} - \frac{6575221}{20577} a^{2} - \frac{121876177}{20577} a - \frac{82332595}{20577} \) |
\( \bigl[a^{2} - a - 5\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{1}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a^{2} - \frac{4}{3} a - \frac{31}{3}\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} + \frac{1}{3} a + \frac{19}{3}\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{1}{3}\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{8}{3}a^{2}-\frac{4}{3}a-\frac{31}{3}\right){x}+\frac{1}{3}a^{3}-\frac{5}{3}a^{2}+\frac{1}{3}a+\frac{19}{3}$ |
| 19.2-a1 |
19.2-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{2} \) |
$12.06050$ |
$(1/3a^3-2/3a^2-8/3a+7/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$48.01809018$ |
1.028139775 |
\( -\frac{508160937943}{361} a^{3} + \frac{1369806856254}{361} a^{2} + \frac{2759155413579}{361} a - \frac{299738575530}{19} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 4\) , \( -\frac{8}{3} a^{3} + \frac{28}{3} a^{2} + \frac{43}{3} a - \frac{92}{3}\) , \( -\frac{1}{3} a^{3} + \frac{20}{3} a^{2} + \frac{14}{3} a - \frac{82}{3}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-\frac{8}{3}a^{3}+\frac{28}{3}a^{2}+\frac{43}{3}a-\frac{92}{3}\right){x}-\frac{1}{3}a^{3}+\frac{20}{3}a^{2}+\frac{14}{3}a-\frac{82}{3}$ |
| 19.2-a2 |
19.2-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{6} \) |
$12.06050$ |
$(1/3a^3-2/3a^2-8/3a+7/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$48.01809018$ |
1.028139775 |
\( -\frac{9402899137}{47045881} a^{3} + \frac{24367557386}{47045881} a^{2} + \frac{52531525021}{47045881} a - \frac{5278845379}{2476099} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{4}{3}\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{4}{3} a - \frac{26}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{7}{3}\) , \( -\frac{163}{3} a^{3} + \frac{440}{3} a^{2} + \frac{878}{3} a - \frac{1807}{3}\) , \( -\frac{1757}{3} a^{3} + \frac{4735}{3} a^{2} + \frac{9535}{3} a - \frac{19682}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{7}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{4}{3}a-\frac{26}{3}\right){x}^{2}+\left(-\frac{163}{3}a^{3}+\frac{440}{3}a^{2}+\frac{878}{3}a-\frac{1807}{3}\right){x}-\frac{1757}{3}a^{3}+\frac{4735}{3}a^{2}+\frac{9535}{3}a-\frac{19682}{3}$ |
| 19.2-b1 |
19.2-b |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( -19 \) |
$12.06050$ |
$(1/3a^3-2/3a^2-8/3a+7/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.042884207$ |
$1265.568406$ |
2.324129283 |
\( \frac{71135}{57} a^{3} - \frac{311215}{57} a^{2} - \frac{429790}{57} a + \frac{42080}{3} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{7}{3}\) , \( a^{2} - a - 5\) , \( -2 a^{3} + 7 a^{2} + 10 a - 29\) , \( \frac{8}{3} a^{3} - \frac{19}{3} a^{2} - \frac{43}{3} a + \frac{74}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{7}{3}\right){x}^{2}+\left(-2a^{3}+7a^{2}+10a-29\right){x}+\frac{8}{3}a^{3}-\frac{19}{3}a^{2}-\frac{43}{3}a+\frac{74}{3}$ |
| 19.2-c1 |
19.2-c |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$12.06050$ |
$(1/3a^3-2/3a^2-8/3a+7/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.016349061$ |
$1185.630756$ |
2.490237769 |
\( \frac{24436934}{20577} a^{3} - \frac{73000453}{20577} a^{2} - \frac{77063008}{20577} a + \frac{10442573}{1083} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{19}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{7}{3} a - \frac{14}{3}\) , \( \frac{4}{3} a^{3} - \frac{8}{3} a^{2} - \frac{26}{3} a + \frac{43}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{4}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{19}{3}\right){x}^{2}+\left(-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{7}{3}a-\frac{14}{3}\right){x}+\frac{4}{3}a^{3}-\frac{8}{3}a^{2}-\frac{26}{3}a+\frac{43}{3}$ |
| 19.3-a1 |
19.3-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{6} \) |
$12.06050$ |
$(1/3a^3-2/3a^2-2/3a+10/3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 2 \cdot 3 \) |
$1$ |
$4.181238845$ |
2.738093815 |
\( \frac{31470834541163641675}{141137643} a^{3} + \frac{17490769409932911355}{141137643} a^{2} - \frac{287496602765861825690}{141137643} a - \frac{20228367865591652465}{7428297} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 5\) , \( -38 a^{3} - 89 a^{2} + 77 a + 201\) , \( -\frac{2317}{3} a^{3} - \frac{5374}{3} a^{2} + \frac{5363}{3} a + \frac{13247}{3}\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-38a^{3}-89a^{2}+77a+201\right){x}-\frac{2317}{3}a^{3}-\frac{5374}{3}a^{2}+\frac{5363}{3}a+\frac{13247}{3}$ |
| 19.3-a2 |
19.3-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{2} \) |
$12.06050$ |
$(1/3a^3-2/3a^2-2/3a+10/3)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 2 \) |
$1$ |
$338.6803464$ |
2.738093815 |
\( -\frac{16399225}{1083} a^{3} + \frac{46978445}{1083} a^{2} + \frac{85669340}{1083} a - \frac{10665910}{57} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{7}{3}\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - \frac{4}{3} a + \frac{20}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{19}{3}\) , \( -\frac{4}{3} a^{3} + \frac{17}{3} a^{2} + \frac{11}{3} a - \frac{49}{3}\) , \( \frac{4}{3} a^{3} - \frac{8}{3} a^{2} - \frac{14}{3} a + \frac{13}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{7}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{19}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-\frac{4}{3}a+\frac{20}{3}\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{17}{3}a^{2}+\frac{11}{3}a-\frac{49}{3}\right){x}+\frac{4}{3}a^{3}-\frac{8}{3}a^{2}-\frac{14}{3}a+\frac{13}{3}$ |
| 19.4-a1 |
19.4-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( 19^{6} \) |
$12.06050$ |
$(2/3a^3-7/3a^2-7/3a+29/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$2.548677142$ |
$4.181238845$ |
2.738093815 |
\( \frac{68522463013409297275}{141137643} a^{3} - \frac{217477364519078789255}{141137643} a^{2} - \frac{212469885007002869060}{141137643} a + \frac{31521808225779997090}{7428297} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{19}{3}\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 4\) , \( -242 a^{3} + 648 a^{2} + 1324 a - 2706\) , \( -\frac{12869}{3} a^{3} + \frac{34669}{3} a^{2} + \frac{69973}{3} a - \frac{144338}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{19}{3}\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-242a^{3}+648a^{2}+1324a-2706\right){x}-\frac{12869}{3}a^{3}+\frac{34669}{3}a^{2}+\frac{69973}{3}a-\frac{144338}{3}$ |
| 19.4-a2 |
19.4-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( 19^{2} \) |
$12.06050$ |
$(2/3a^3-7/3a^2-7/3a+29/3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.849559047$ |
$338.6803464$ |
2.738093815 |
\( -\frac{994825}{1083} a^{3} - \frac{12190345}{1083} a^{2} + \frac{1300910}{1083} a + \frac{1726235}{57} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{19}{3}\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 4\) , \( \frac{14}{3} a^{3} - \frac{46}{3} a^{2} - \frac{73}{3} a + \frac{212}{3}\) , \( -\frac{73}{3} a^{3} + \frac{200}{3} a^{2} + \frac{389}{3} a - \frac{847}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{19}{3}\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(\frac{14}{3}a^{3}-\frac{46}{3}a^{2}-\frac{73}{3}a+\frac{212}{3}\right){x}-\frac{73}{3}a^{3}+\frac{200}{3}a^{2}+\frac{389}{3}a-\frac{847}{3}$ |
| 31.1-a1 |
31.1-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.1 |
\( 31 \) |
\( - 31^{3} \) |
$12.82158$ |
$(a^3-3a^2-4a+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.073140515$ |
$333.3571096$ |
3.132321051 |
\( \frac{4263093341890}{29791} a^{3} + \frac{9862773307340}{29791} a^{2} - \frac{9950473600627}{29791} a - \frac{24444943613049}{29791} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{4}{3}\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - \frac{7}{3} a + \frac{23}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( \frac{61}{3} a^{3} - \frac{164}{3} a^{2} - \frac{338}{3} a + \frac{697}{3}\) , \( -107 a^{3} + 287 a^{2} + 582 a - 1197\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{4}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-\frac{7}{3}a+\frac{23}{3}\right){x}^{2}+\left(\frac{61}{3}a^{3}-\frac{164}{3}a^{2}-\frac{338}{3}a+\frac{697}{3}\right){x}-107a^{3}+287a^{2}+582a-1197$ |
| 31.2-a1 |
31.2-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( - 31^{3} \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+13/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.073140515$ |
$333.3571096$ |
3.132321051 |
\( \frac{79321153107853}{89373} a^{3} - \frac{213809186189066}{89373} a^{2} - \frac{430700744865734}{89373} a + \frac{888890200496374}{89373} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( -a^{2} + 6\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{16}{3}\) , \( a^{2} + 3 a + 7\) , \( -\frac{5}{3} a^{3} - \frac{23}{3} a^{2} + \frac{22}{3} a + \frac{85}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(a^{2}+3a+7\right){x}-\frac{5}{3}a^{3}-\frac{23}{3}a^{2}+\frac{22}{3}a+\frac{85}{3}$ |
| 31.3-a1 |
31.3-a |
$4$ |
$6$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.3 |
\( 31 \) |
\( - 31^{2} \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+1/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$89.02684753$ |
1.906199156 |
\( \frac{2491035988092800140}{2883} a^{3} - \frac{6714556230303461069}{2883} a^{2} - \frac{13525914094484185007}{2883} a + \frac{27915089502625861798}{2883} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{19}{3}\) , \( 3 a^{3} - 8 a^{2} + 9\) , \( -8 a^{3} + 26 a^{2} + 46 a - 107\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{19}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{4}{3}\right){x}^{2}+\left(3a^{3}-8a^{2}+9\right){x}-8a^{3}+26a^{2}+46a-107$ |
| 31.3-a2 |
31.3-a |
$4$ |
$6$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.3 |
\( 31 \) |
\( -31 \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+1/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$712.2147802$ |
1.906199156 |
\( \frac{976696043}{93} a^{3} - \frac{2632199845}{93} a^{2} - \frac{5308382326}{93} a + \frac{10956705821}{93} \) |
\( \bigl[a^{2} - a - 4\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{2}{3} a + \frac{22}{3}\) , \( a^{2} - 4\) , \( -\frac{4}{3} a^{3} + \frac{2}{3} a^{2} + \frac{29}{3} a - \frac{7}{3}\) , \( -\frac{13}{3} a^{3} + \frac{29}{3} a^{2} + \frac{68}{3} a - \frac{106}{3}\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{2}{3}a+\frac{22}{3}\right){x}^{2}+\left(-\frac{4}{3}a^{3}+\frac{2}{3}a^{2}+\frac{29}{3}a-\frac{7}{3}\right){x}-\frac{13}{3}a^{3}+\frac{29}{3}a^{2}+\frac{68}{3}a-\frac{106}{3}$ |
| 31.3-a3 |
31.3-a |
$4$ |
$6$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.3 |
\( 31 \) |
\( - 31^{3} \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+1/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$712.2147802$ |
1.906199156 |
\( -\frac{339114413}{89373} a^{3} + \frac{217637485}{89373} a^{2} + \frac{2413788172}{89373} a + \frac{1971064906}{89373} \) |
\( \bigl[a + 1\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - \frac{7}{3} a + \frac{26}{3}\) , \( a^{2} - a - 5\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{25}{3} a - \frac{40}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{25}{3} a + \frac{49}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-\frac{7}{3}a+\frac{26}{3}\right){x}^{2}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{25}{3}a-\frac{40}{3}\right){x}-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{25}{3}a+\frac{49}{3}$ |
| 31.3-a4 |
31.3-a |
$4$ |
$6$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.3 |
\( 31 \) |
\( - 31^{6} \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+1/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$89.02684753$ |
1.906199156 |
\( -\frac{46388460705952858}{2662511043} a^{3} + \frac{147261576990304325}{2662511043} a^{2} + \frac{143687688969009251}{2662511043} a - \frac{405300633423132487}{2662511043} \) |
\( \bigl[a + 1\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - \frac{7}{3} a + \frac{26}{3}\) , \( a^{2} - a - 5\) , \( -a^{3} + 5 a + 5\) , \( -\frac{26}{3} a^{3} - \frac{20}{3} a^{2} + \frac{223}{3} a + \frac{307}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-\frac{7}{3}a+\frac{26}{3}\right){x}^{2}+\left(-a^{3}+5a+5\right){x}-\frac{26}{3}a^{3}-\frac{20}{3}a^{2}+\frac{223}{3}a+\frac{307}{3}$ |
| 31.3-b1 |
31.3-b |
$4$ |
$4$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.3 |
\( 31 \) |
\( 31^{2} \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+1/3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$98.53127417$ |
0.527425818 |
\( -\frac{44625886081565}{961} a^{3} - \frac{24803238677698}{961} a^{2} + \frac{407673746226817}{961} a + \frac{545004213774326}{961} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{7}{3} a - \frac{23}{3}\) , \( 1\) , \( 7 a^{3} + 8 a^{2} - 72 a - 110\) , \( \frac{103}{3} a^{3} + \frac{43}{3} a^{2} - \frac{1052}{3} a - \frac{1406}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){x}{y}+{y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{7}{3}a-\frac{23}{3}\right){x}^{2}+\left(7a^{3}+8a^{2}-72a-110\right){x}+\frac{103}{3}a^{3}+\frac{43}{3}a^{2}-\frac{1052}{3}a-\frac{1406}{3}$ |
| 31.3-b2 |
31.3-b |
$4$ |
$4$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.3 |
\( 31 \) |
\( - 31^{4} \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+1/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$6.158204635$ |
0.527425818 |
\( \frac{3128833984726809217}{2770563} a^{3} - \frac{8433722616666026492}{2770563} a^{2} - \frac{16989077299433804945}{2770563} a + \frac{35062404466030137901}{2770563} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{7}{3} a - \frac{23}{3}\) , \( 1\) , \( -\frac{19}{3} a^{3} - \frac{76}{3} a^{2} - \frac{121}{3} a - \frac{85}{3}\) , \( -\frac{496}{3} a^{3} - \frac{1384}{3} a^{2} + \frac{341}{3} a + \frac{2135}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){x}{y}+{y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{7}{3}a-\frac{23}{3}\right){x}^{2}+\left(-\frac{19}{3}a^{3}-\frac{76}{3}a^{2}-\frac{121}{3}a-\frac{85}{3}\right){x}-\frac{496}{3}a^{3}-\frac{1384}{3}a^{2}+\frac{341}{3}a+\frac{2135}{3}$ |
| 31.3-b3 |
31.3-b |
$4$ |
$4$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.3 |
\( 31 \) |
\( -31 \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+1/3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$788.2501934$ |
0.527425818 |
\( -\frac{4396579}{93} a^{3} - \frac{2227402}{93} a^{2} + \frac{39776807}{93} a + \frac{52655981}{93} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{7}{3} a - \frac{23}{3}\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{19}{3} a^{2} - \frac{11}{3} a - \frac{65}{3}\) , \( a^{3} + 7 a^{2} - 5 a - 24\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){x}{y}+{y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{7}{3}a-\frac{23}{3}\right){x}^{2}+\left(\frac{1}{3}a^{3}+\frac{19}{3}a^{2}-\frac{11}{3}a-\frac{65}{3}\right){x}+a^{3}+7a^{2}-5a-24$ |
| 31.3-b4 |
31.3-b |
$4$ |
$4$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.3 |
\( 31 \) |
\( 31 \) |
$12.82158$ |
$(1/3a^3-2/3a^2-2/3a+1/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$12.31640927$ |
0.527425818 |
\( -\frac{1424835233324713273792949}{31} a^{3} - \frac{791890984837917843634900}{31} a^{2} + \frac{13016346367251490917814021}{31} a + \frac{17400864880967627952306143}{31} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{1}{3}\) , \( a^{2} - a - 4\) , \( -\frac{94}{3} a^{3} + \frac{272}{3} a^{2} + \frac{410}{3} a - \frac{937}{3}\) , \( \frac{115}{3} a^{3} - \frac{533}{3} a^{2} + \frac{463}{3} a + \frac{127}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{1}{3}\right){x}^{2}+\left(-\frac{94}{3}a^{3}+\frac{272}{3}a^{2}+\frac{410}{3}a-\frac{937}{3}\right){x}+\frac{115}{3}a^{3}-\frac{533}{3}a^{2}+\frac{463}{3}a+\frac{127}{3}$ |
| 31.4-a1 |
31.4-a |
$4$ |
$6$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.4 |
\( 31 \) |
\( - 31^{3} \) |
$12.82158$ |
$(-2/3a^3+4/3a^2+13/3a-8/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$712.2147802$ |
1.906199156 |
\( -\frac{186766795}{29791} a^{3} + \frac{527064037}{29791} a^{2} + \frac{694428606}{29791} a - \frac{1240852989}{29791} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} + \frac{1}{3} a + \frac{22}{3}\) , \( a^{2} - 5\) , \( \frac{4}{3} a^{3} - \frac{5}{3} a^{2} - \frac{11}{3} a + \frac{40}{3}\) , \( -3 a^{3} + 14 a^{2} + 19 a - 49\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}+\frac{1}{3}a+\frac{22}{3}\right){x}^{2}+\left(\frac{4}{3}a^{3}-\frac{5}{3}a^{2}-\frac{11}{3}a+\frac{40}{3}\right){x}-3a^{3}+14a^{2}+19a-49$ |
| 31.4-a2 |
31.4-a |
$4$ |
$6$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.4 |
\( 31 \) |
\( -31 \) |
$12.82158$ |
$(-2/3a^3+4/3a^2+13/3a-8/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$712.2147802$ |
1.906199156 |
\( \frac{52084749}{31} a^{3} + \frac{122099755}{31} a^{2} - \frac{118789708}{31} a - \frac{298552194}{31} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - 2 a - 4\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -a^{3} + 2 a^{2} + a - 8\) , \( -\frac{5}{3} a^{3} + \frac{1}{3} a^{2} + \frac{19}{3} a + \frac{4}{3}\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-a^{3}+2a^{2}+a-8\right){x}-\frac{5}{3}a^{3}+\frac{1}{3}a^{2}+\frac{19}{3}a+\frac{4}{3}$ |
| 31.4-a3 |
31.4-a |
$4$ |
$6$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.4 |
\( 31 \) |
\( - 31^{2} \) |
$12.82158$ |
$(-2/3a^3+4/3a^2+13/3a-8/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$89.02684753$ |
1.906199156 |
\( \frac{133880116433848194}{961} a^{3} + \frac{309734518504923875}{961} a^{2} - \frac{312489197495846201}{961} a - \frac{767679418657891403}{961} \) |
\( \bigl[a^{2} - 4\) , \( -\frac{2}{3} a^{3} + \frac{7}{3} a^{2} + \frac{7}{3} a - \frac{26}{3}\) , \( a^{2} - 5\) , \( 2 a^{3} + 4 a^{2} - 22 a - 40\) , \( -\frac{10}{3} a^{3} - \frac{16}{3} a^{2} + \frac{41}{3} a + \frac{68}{3}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}+\frac{7}{3}a^{2}+\frac{7}{3}a-\frac{26}{3}\right){x}^{2}+\left(2a^{3}+4a^{2}-22a-40\right){x}-\frac{10}{3}a^{3}-\frac{16}{3}a^{2}+\frac{41}{3}a+\frac{68}{3}$ |
| 31.4-a4 |
31.4-a |
$4$ |
$6$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.4 |
\( 31 \) |
\( - 31^{6} \) |
$12.82158$ |
$(-2/3a^3+4/3a^2+13/3a-8/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1$ |
$89.02684753$ |
1.906199156 |
\( -\frac{7107336660379754}{887503681} a^{3} - \frac{3946878538706695}{887503681} a^{2} + \frac{64954888155483783}{887503681} a + \frac{86842140618716722}{887503681} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{2}{3} a - \frac{1}{3}\) , \( 0\) , \( -4 a^{3} + 12 a^{2} + 16 a - 40\) , \( -\frac{71}{3} a^{3} + \frac{220}{3} a^{2} + \frac{247}{3} a - \frac{653}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{4}{3}\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{2}{3}a-\frac{1}{3}\right){x}^{2}+\left(-4a^{3}+12a^{2}+16a-40\right){x}-\frac{71}{3}a^{3}+\frac{220}{3}a^{2}+\frac{247}{3}a-\frac{653}{3}$ |
| 31.4-b1 |
31.4-b |
$4$ |
$4$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.4 |
\( 31 \) |
\( 31^{2} \) |
$12.82158$ |
$(-2/3a^3+4/3a^2+13/3a-8/3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$98.53127417$ |
0.527425818 |
\( -\frac{97166124982729}{961} a^{3} + \frac{308387260806286}{961} a^{2} + \frac{301286309094653}{961} a - \frac{849272556101274}{961} \) |
\( \bigl[a^{2} - a - 5\) , \( a + 1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{19}{3}\) , \( -39 a^{3} + 103 a^{2} + 221 a - 436\) , \( -\frac{641}{3} a^{3} + \frac{1717}{3} a^{2} + \frac{3523}{3} a - \frac{7193}{3}\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{19}{3}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-39a^{3}+103a^{2}+221a-436\right){x}-\frac{641}{3}a^{3}+\frac{1717}{3}a^{2}+\frac{3523}{3}a-\frac{7193}{3}$ |
| 31.4-b2 |
31.4-b |
$4$ |
$4$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.4 |
\( 31 \) |
\( -31 \) |
$12.82158$ |
$(-2/3a^3+4/3a^2+13/3a-8/3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$788.2501934$ |
0.527425818 |
\( -\frac{3161945}{31} a^{3} + \frac{9997410}{31} a^{2} + \frac{9878421}{31} a - \frac{27384617}{31} \) |
\( \bigl[a^{2} - a - 5\) , \( a + 1\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{19}{3}\) , \( 6 a^{3} - 17 a^{2} - 29 a + 74\) , \( -23 a^{3} + 61 a^{2} + 128 a - 250\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{19}{3}\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a^{3}-17a^{2}-29a+74\right){x}-23a^{3}+61a^{2}+128a-250$ |
| 31.4-b3 |
31.4-b |
$4$ |
$4$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.4 |
\( 31 \) |
\( - 31^{4} \) |
$12.82158$ |
$(-2/3a^3+4/3a^2+13/3a-8/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$6.158204635$ |
0.527425818 |
\( \frac{168158959638160513}{923521} a^{3} + \frac{389033629794481660}{923521} a^{2} - \frac{392492339590882945}{923521} a - \frac{964195699855942789}{923521} \) |
\( \bigl[a^{2} - 4\) , \( 0\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( -72 a^{3} + 191 a^{2} + 434 a - 875\) , \( -\frac{2560}{3} a^{3} + \frac{6788}{3} a^{2} + \frac{14555}{3} a - \frac{29467}{3}\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){y}={x}^{3}+\left(-72a^{3}+191a^{2}+434a-875\right){x}-\frac{2560}{3}a^{3}+\frac{6788}{3}a^{2}+\frac{14555}{3}a-\frac{29467}{3}$ |
| 31.4-b4 |
31.4-b |
$4$ |
$4$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
31.4 |
\( 31 \) |
\( 31 \) |
$12.82158$ |
$(-2/3a^3+4/3a^2+13/3a-8/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 1 \) |
$1$ |
$12.31640927$ |
0.527425818 |
\( -\frac{3102339951269416148730655}{31} a^{3} + \frac{9846241354026176688682108}{31} a^{2} + \frac{9619529555719156194803999}{31} a - \frac{27115721208031391693244981}{31} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{4}{3}\) , \( -a^{2} + 5\) , \( 1\) , \( -\frac{29}{3} a^{3} - \frac{26}{3} a^{2} + \frac{202}{3} a + \frac{277}{3}\) , \( 44 a^{3} - 7 a^{2} - 518 a - 644\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{4}{3}\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-\frac{29}{3}a^{3}-\frac{26}{3}a^{2}+\frac{202}{3}a+\frac{277}{3}\right){x}+44a^{3}-7a^{2}-518a-644$ |
| 59.1-a1 |
59.1-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( -59 \) |
$13.89561$ |
$(2/3a^3-1/3a^2-10/3a-1/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$203.3937357$ |
2.177483412 |
\( \frac{5032381833266}{59} a^{3} + \frac{2796778767836}{59} a^{2} - \frac{45972321997094}{59} a - \frac{61457604170365}{59} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 4\) , \( a^{2} - 5\) , \( -\frac{547}{3} a^{3} + \frac{1466}{3} a^{2} + \frac{2984}{3} a - \frac{6133}{3}\) , \( -\frac{4334}{3} a^{3} + \frac{11674}{3} a^{2} + \frac{23560}{3} a - \frac{48593}{3}\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-\frac{547}{3}a^{3}+\frac{1466}{3}a^{2}+\frac{2984}{3}a-\frac{6133}{3}\right){x}-\frac{4334}{3}a^{3}+\frac{11674}{3}a^{2}+\frac{23560}{3}a-\frac{48593}{3}$ |
| 59.1-a2 |
59.1-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
59.1 |
\( 59 \) |
\( - 59^{3} \) |
$13.89561$ |
$(2/3a^3-1/3a^2-10/3a-1/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$203.3937357$ |
2.177483412 |
\( \frac{66993920059020}{205379} a^{3} - \frac{180580915668917}{205379} a^{2} - \frac{363766336999886}{205379} a + \frac{750745823943358}{205379} \) |
\( \bigl[a\) , \( -a^{2} + 4\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( -5 a^{3} + 14 a^{2} + 27 a - 58\) , \( -\frac{47}{3} a^{3} + \frac{124}{3} a^{2} + \frac{262}{3} a - \frac{530}{3}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-5a^{3}+14a^{2}+27a-58\right){x}-\frac{47}{3}a^{3}+\frac{124}{3}a^{2}+\frac{262}{3}a-\frac{530}{3}$ |
| 59.2-a1 |
59.2-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( -59 \) |
$13.89561$ |
$(a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$203.3937357$ |
2.177483412 |
\( \frac{32871359972138}{177} a^{3} - \frac{104327347247380}{177} a^{2} - \frac{101925561368398}{177} a + \frac{287308334523221}{177} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{19}{3}\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + \frac{2}{3} a - \frac{7}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{19}{3}\) , \( -\frac{88}{3} a^{3} - \frac{202}{3} a^{2} + \frac{185}{3} a + \frac{458}{3}\) , \( -232 a^{3} - 539 a^{2} + 529 a + 1314\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{19}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{19}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}+\frac{2}{3}a^{2}+\frac{2}{3}a-\frac{7}{3}\right){x}^{2}+\left(-\frac{88}{3}a^{3}-\frac{202}{3}a^{2}+\frac{185}{3}a+\frac{458}{3}\right){x}-232a^{3}-539a^{2}+529a+1314$ |
| 59.2-a2 |
59.2-a |
$2$ |
$3$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
59.2 |
\( 59 \) |
\( - 59^{3} \) |
$13.89561$ |
$(a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$203.3937357$ |
2.177483412 |
\( \frac{32405796819643}{616137} a^{3} + \frac{74967633013345}{616137} a^{2} - \frac{75638773983857}{616137} a - \frac{185807311545524}{616137} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{7}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{4}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -a^{3} - 2 a^{2} + 3 a + 6\) , \( -\frac{11}{3} a^{3} - \frac{26}{3} a^{2} + \frac{16}{3} a + \frac{46}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{7}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{4}{3}\right){x}^{2}+\left(-a^{3}-2a^{2}+3a+6\right){x}-\frac{11}{3}a^{3}-\frac{26}{3}a^{2}+\frac{16}{3}a+\frac{46}{3}$ |
| 61.1-a1 |
61.1-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
61.1 |
\( 61 \) |
\( 61 \) |
$13.95364$ |
$(-2/3a^3+7/3a^2+7/3a-32/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 1 \) |
$1$ |
$49.95754113$ |
2.139332693 |
\( \frac{220328171919}{61} a^{3} - \frac{593883984343}{61} a^{2} - \frac{1196354326466}{61} a + \frac{2468988277076}{61} \) |
\( \bigl[\frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{2}{3} a + \frac{7}{3}\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} + \frac{1}{3} a + \frac{19}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{4}{3}\) , \( \frac{13}{3} a^{3} + \frac{10}{3} a^{2} - \frac{119}{3} a - \frac{167}{3}\) , \( \frac{74}{3} a^{3} + \frac{38}{3} a^{2} - \frac{676}{3} a - \frac{895}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{2}{3}a+\frac{7}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}+\frac{1}{3}a+\frac{19}{3}\right){x}^{2}+\left(\frac{13}{3}a^{3}+\frac{10}{3}a^{2}-\frac{119}{3}a-\frac{167}{3}\right){x}+\frac{74}{3}a^{3}+\frac{38}{3}a^{2}-\frac{676}{3}a-\frac{895}{3}$ |
| 61.2-a1 |
61.2-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
61.2 |
\( 61 \) |
\( 61 \) |
$13.95364$ |
$(a^2-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$4$ |
\( 1 \) |
$1$ |
$49.95754113$ |
2.139332693 |
\( \frac{106588127371}{183} a^{3} + \frac{246506666773}{183} a^{2} - \frac{248800236242}{183} a - \frac{610956181109}{183} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{19}{3}\) , \( a^{2} - 2 a - 5\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( -7 a^{3} + 18 a^{2} + 42 a - 73\) , \( -\frac{14}{3} a^{3} + \frac{37}{3} a^{2} + \frac{103}{3} a - \frac{215}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{19}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-7a^{3}+18a^{2}+42a-73\right){x}-\frac{14}{3}a^{3}+\frac{37}{3}a^{2}+\frac{103}{3}a-\frac{215}{3}$ |
| 79.1-a1 |
79.1-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( 79^{3} \) |
$14.41201$ |
$(1/3a^3+1/3a^2-5/3a-11/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$265.2593838$ |
2.839801855 |
\( -\frac{1966001364}{493039} a^{3} + \frac{5240220034}{493039} a^{2} + \frac{10630896835}{493039} a - \frac{21818376647}{493039} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - \frac{4}{3} a + \frac{26}{3}\) , \( -\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{16}{3}\) , \( -\frac{11}{3} a^{3} + \frac{40}{3} a^{2} + \frac{64}{3} a - \frac{143}{3}\) , \( 7 a^{3} - 12 a^{2} - 32 a + 54\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){x}{y}+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{16}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-\frac{4}{3}a+\frac{26}{3}\right){x}^{2}+\left(-\frac{11}{3}a^{3}+\frac{40}{3}a^{2}+\frac{64}{3}a-\frac{143}{3}\right){x}+7a^{3}-12a^{2}-32a+54$ |
| 79.1-b1 |
79.1-b |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
79.1 |
\( 79 \) |
\( -79 \) |
$14.41201$ |
$(1/3a^3+1/3a^2-5/3a-11/3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.034131972$ |
$835.1099446$ |
4.882500554 |
\( -\frac{5620}{79} a^{3} + \frac{28625}{79} a^{2} - \frac{70505}{79} a - \frac{208205}{79} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 4\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{7}{3} a^{2} - \frac{8}{3} a - \frac{14}{3}\) , \( \frac{1}{3} a^{3} + \frac{7}{3} a^{2} - \frac{5}{3} a - \frac{20}{3}\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+{y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(\frac{1}{3}a^{3}+\frac{7}{3}a^{2}-\frac{8}{3}a-\frac{14}{3}\right){x}+\frac{1}{3}a^{3}+\frac{7}{3}a^{2}-\frac{5}{3}a-\frac{20}{3}$ |
| 79.2-a1 |
79.2-a |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( 79^{3} \) |
$14.41201$ |
$(1/3a^3-2/3a^2-2/3a-5/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$265.2593838$ |
2.839801855 |
\( -\frac{1172462159}{1479117} a^{3} - \frac{1579727600}{1479117} a^{2} + \frac{3459640750}{1479117} a + \frac{2945530852}{1479117} \) |
\( \bigl[a + 1\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - \frac{2}{3} a + \frac{19}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{7}{3}\) , \( -a^{3} + 7 a + 8\) , \( -3 a^{3} - 2 a^{2} + 28 a + 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{7}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}-\frac{5}{3}a^{2}-\frac{2}{3}a+\frac{19}{3}\right){x}^{2}+\left(-a^{3}+7a+8\right){x}-3a^{3}-2a^{2}+28a+38$ |
| 79.2-b1 |
79.2-b |
$1$ |
$1$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
79.2 |
\( 79 \) |
\( -79 \) |
$14.41201$ |
$(1/3a^3-2/3a^2-2/3a-5/3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.034131972$ |
$835.1099446$ |
4.882500554 |
\( -\frac{63310}{237} a^{3} + \frac{74465}{237} a^{2} + \frac{612365}{237} a - \frac{480370}{237} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{5}{3} a - \frac{19}{3}\) , \( a^{2} - 2 a - 5\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - \frac{5}{3} a + \frac{4}{3}\) , \( 2 a + 6\) , \( 2 a^{3} - 4 a^{2} - 8 a + 8\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{5}{3}a-\frac{19}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}-\frac{5}{3}a+\frac{4}{3}\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(2a+6\right){x}+2a^{3}-4a^{2}-8a+8$ |
| 81.1-a1 |
81.1-a |
$2$ |
$2$ |
4.4.8725.1 |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{18} \) |
$14.45712$ |
$(-a^2+4), (2/3a^3-7/3a^2-7/3a+26/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.458329769$ |
$28.65076511$ |
3.578485275 |
\( \frac{2937821716}{243} a^{3} + \frac{44347329953}{6561} a^{2} - \frac{724926526250}{6561} a - \frac{970586118283}{6561} \) |
\( \bigl[-\frac{1}{3} a^{3} + \frac{5}{3} a^{2} + \frac{2}{3} a - \frac{16}{3}\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - \frac{10}{3} a + \frac{20}{3}\) , \( a + 1\) , \( -94 a^{3} + 253 a^{2} + 510 a - 1051\) , \( -\frac{3185}{3} a^{3} + \frac{8584}{3} a^{2} + \frac{17293}{3} a - \frac{35693}{3}\bigr] \) |
${y}^2+\left(-\frac{1}{3}a^{3}+\frac{5}{3}a^{2}+\frac{2}{3}a-\frac{16}{3}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}-\frac{7}{3}a^{2}-\frac{10}{3}a+\frac{20}{3}\right){x}^{2}+\left(-94a^{3}+253a^{2}+510a-1051\right){x}-\frac{3185}{3}a^{3}+\frac{8584}{3}a^{2}+\frac{17293}{3}a-\frac{35693}{3}$ |
*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.
