| 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 |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$14.27074$ |
$(1/3a^3+1/3a^2-11/3a-2/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.285634779$ |
$1146.144250$ |
2.697880542 |
\( \frac{3929344}{3} a^{3} + \frac{7518176}{3} a^{2} - \frac{29180800}{3} a - \frac{41805617}{3} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{26}{3}\) , \( -a^{2} - a + 6\) , \( a + 1\) , \( -\frac{2}{3} a^{3} - \frac{14}{3} a^{2} + \frac{7}{3} a + \frac{109}{3}\) , \( \frac{10}{3} a^{3} + \frac{7}{3} a^{2} - \frac{83}{3} a - \frac{14}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{26}{3}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{14}{3}a^{2}+\frac{7}{3}a+\frac{109}{3}\right){x}+\frac{10}{3}a^{3}+\frac{7}{3}a^{2}-\frac{83}{3}a-\frac{14}{3}$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$14.27074$ |
$(1/3a^3+1/3a^2-11/3a-2/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.047605796$ |
$1146.144250$ |
2.697880542 |
\( -\frac{19114295080}{81} a^{3} - \frac{271377365096}{729} a^{2} + \frac{1536956225327}{729} a + \frac{2069232762883}{729} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{5}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( -\frac{5}{3} a^{3} + \frac{10}{3} a^{2} + \frac{55}{3} a - \frac{125}{3}\) , \( \frac{13}{3} a^{3} - \frac{35}{3} a^{2} - \frac{122}{3} a + \frac{325}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{5}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){x}^{2}+\left(-\frac{5}{3}a^{3}+\frac{10}{3}a^{2}+\frac{55}{3}a-\frac{125}{3}\right){x}+\frac{13}{3}a^{3}-\frac{35}{3}a^{2}-\frac{122}{3}a+\frac{325}{3}$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.27074$ |
$(1/3a^3+1/3a^2-11/3a-2/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.095211593$ |
$1146.144250$ |
2.697880542 |
\( -\frac{147376}{27} a^{3} - \frac{229045}{27} a^{2} + \frac{1326526}{27} a + \frac{1778563}{27} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{5}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{5}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){x}^{2}$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$14.27074$ |
$(1/3a^3+1/3a^2-11/3a-2/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.142817389$ |
$1146.144250$ |
2.697880542 |
\( 14897336330890 a^{3} + \frac{256222731566666}{9} a^{2} - \frac{997117402281392}{9} a - \frac{1427798067959857}{9} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{17}{3} a^{3} + \frac{23}{3} a^{2} - \frac{160}{3} a - \frac{205}{3}\) , \( 2 a^{3} + 3 a^{2} - 17 a - 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(\frac{17}{3}a^{3}+\frac{23}{3}a^{2}-\frac{160}{3}a-\frac{205}{3}\right){x}+2a^{3}+3a^{2}-17a-23$ |
| 9.1-b1 |
9.1-b |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$14.27074$ |
$(1/3a^3+1/3a^2-11/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$925.2797820$ |
1.906274461 |
\( \frac{3929344}{3} a^{3} + \frac{7518176}{3} a^{2} - \frac{29180800}{3} a - \frac{41805617}{3} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{34}{3}\) , \( -\frac{1}{3} a^{3} - \frac{4}{3} a^{2} + \frac{5}{3} a + \frac{29}{3}\) , \( 0\) , \( a^{3} - 2 a^{2} - 10 a + 22\) , \( 0\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{34}{3}\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{4}{3}a^{2}+\frac{5}{3}a+\frac{29}{3}\right){x}^{2}+\left(a^{3}-2a^{2}-10a+22\right){x}$ |
| 9.1-b2 |
9.1-b |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$14.27074$ |
$(1/3a^3+1/3a^2-11/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$462.6398910$ |
1.906274461 |
\( 14897336330890 a^{3} + \frac{256222731566666}{9} a^{2} - \frac{997117402281392}{9} a - \frac{1427798067959857}{9} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{16}{3} a + \frac{34}{3}\) , \( 0\) , \( 4 a - 12\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} + \frac{38}{3} a - \frac{100}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}={x}^{3}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{16}{3}a+\frac{34}{3}\right){x}^{2}+\left(4a-12\right){x}+\frac{2}{3}a^{3}-\frac{7}{3}a^{2}+\frac{38}{3}a-\frac{100}{3}$ |
| 9.1-b3 |
9.1-b |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.27074$ |
$(1/3a^3+1/3a^2-11/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$925.2797820$ |
1.906274461 |
\( -\frac{147376}{27} a^{3} - \frac{229045}{27} a^{2} + \frac{1326526}{27} a + \frac{1778563}{27} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} - \frac{4}{3} a^{2} + \frac{8}{3} a + \frac{26}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{13}{3} a + \frac{34}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{4}{3}a^{2}+\frac{8}{3}a+\frac{26}{3}\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{13}{3}a+\frac{34}{3}\right){x}+\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}$ |
| 9.1-b4 |
9.1-b |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$14.27074$ |
$(1/3a^3+1/3a^2-11/3a-2/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$462.6398910$ |
1.906274461 |
\( -\frac{19114295080}{81} a^{3} - \frac{271377365096}{729} a^{2} + \frac{1536956225327}{729} a + \frac{2069232762883}{729} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} - \frac{4}{3} a^{2} + \frac{8}{3} a + \frac{26}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( -\frac{17}{3} a^{3} - \frac{35}{3} a^{2} + \frac{118}{3} a + \frac{184}{3}\) , \( 33 a^{3} + 62 a^{2} - 250 a - 355\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{4}{3}a^{2}+\frac{8}{3}a+\frac{26}{3}\right){x}^{2}+\left(-\frac{17}{3}a^{3}-\frac{35}{3}a^{2}+\frac{118}{3}a+\frac{184}{3}\right){x}+33a^{3}+62a^{2}-250a-355$ |
| 9.2-a1 |
9.2-a |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{2} \) |
$14.27074$ |
$(a^3+2a^2-7a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.285634779$ |
$1146.144250$ |
2.697880542 |
\( \frac{3275488}{9} a^{3} - \frac{7491008}{9} a^{2} - \frac{32965760}{9} a + \frac{78643309}{9} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{34}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{37}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( 2 a^{3} + 5 a^{2} - 14 a - 30\) , \( \frac{11}{3} a^{3} + \frac{11}{3} a^{2} - \frac{85}{3} a - \frac{43}{3}\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{34}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{37}{3}\right){x}^{2}+\left(2a^{3}+5a^{2}-14a-30\right){x}+\frac{11}{3}a^{3}+\frac{11}{3}a^{2}-\frac{85}{3}a-\frac{43}{3}$ |
| 9.2-a2 |
9.2-a |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$14.27074$ |
$(a^3+2a^2-7a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.142817389$ |
$1146.144250$ |
2.697880542 |
\( \frac{111278780710750}{27} a^{3} - \frac{255161333055218}{27} a^{2} - \frac{1116702686314064}{27} a + \frac{2667954003726349}{27} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -a^{2} - a + 6\) , \( a + 1\) , \( -4 a^{2} + 8 a + 5\) , \( -2 a^{2} + a + 10\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}-a+6\right){x}^{2}+\left(-4a^{2}+8a+5\right){x}-2a^{2}+a+10$ |
| 9.2-a3 |
9.2-a |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.27074$ |
$(a^3+2a^2-7a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.095211593$ |
$1146.144250$ |
2.697880542 |
\( -\frac{49603}{81} a^{3} + \frac{195404}{81} a^{2} - \frac{45730}{81} a - \frac{302041}{81} \) |
\( \bigl[a\) , \( -a^{2} + 5\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{31}{3}\) , \( -\frac{4}{3} a^{3} - \frac{7}{3} a^{2} + \frac{29}{3} a + \frac{50}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{31}{3}\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-\frac{4}{3}a^{3}-\frac{7}{3}a^{2}+\frac{29}{3}a+\frac{50}{3}\right){x}+\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}$ |
| 9.2-a4 |
9.2-a |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$14.27074$ |
$(a^3+2a^2-7a-11)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.047605796$ |
$1146.144250$ |
2.697880542 |
\( -\frac{57312859465}{2187} a^{3} + \frac{240733268663}{2187} a^{2} - \frac{23678062981}{2187} a - \frac{556859171746}{2187} \) |
\( \bigl[a\) , \( -a^{2} + 5\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{31}{3}\) , \( -\frac{19}{3} a^{3} - \frac{37}{3} a^{2} + \frac{134}{3} a + \frac{200}{3}\) , \( \frac{71}{3} a^{3} + \frac{134}{3} a^{2} - \frac{535}{3} a - \frac{763}{3}\bigr] \) |
${y}^2+a{x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{31}{3}\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-\frac{19}{3}a^{3}-\frac{37}{3}a^{2}+\frac{134}{3}a+\frac{200}{3}\right){x}+\frac{71}{3}a^{3}+\frac{134}{3}a^{2}-\frac{535}{3}a-\frac{763}{3}$ |
| 9.2-b1 |
9.2-b |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{2} \) |
$14.27074$ |
$(a^3+2a^2-7a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$925.2797820$ |
1.906274461 |
\( \frac{3275488}{9} a^{3} - \frac{7491008}{9} a^{2} - \frac{32965760}{9} a + \frac{78643309}{9} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{26}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{5}{3} a - \frac{26}{3}\) , \( 0\) , \( \frac{10}{3} a^{3} + \frac{19}{3} a^{2} - \frac{74}{3} a - \frac{104}{3}\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{26}{3}\right){x}{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{5}{3}a-\frac{26}{3}\right){x}^{2}+\left(\frac{10}{3}a^{3}+\frac{19}{3}a^{2}-\frac{74}{3}a-\frac{104}{3}\right){x}$ |
| 9.2-b2 |
9.2-b |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{12} \) |
$14.27074$ |
$(a^3+2a^2-7a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$462.6398910$ |
1.906274461 |
\( -\frac{57312859465}{2187} a^{3} + \frac{240733268663}{2187} a^{2} - \frac{23678062981}{2187} a - \frac{556859171746}{2187} \) |
\( \bigl[1\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{34}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( -\frac{5}{3} a^{3} + \frac{13}{3} a^{2} + \frac{58}{3} a - \frac{146}{3}\) , \( \frac{26}{3} a^{3} - \frac{61}{3} a^{2} - \frac{250}{3} a + \frac{605}{3}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{34}{3}\right){x}^{2}+\left(-\frac{5}{3}a^{3}+\frac{13}{3}a^{2}+\frac{58}{3}a-\frac{146}{3}\right){x}+\frac{26}{3}a^{3}-\frac{61}{3}a^{2}-\frac{250}{3}a+\frac{605}{3}$ |
| 9.2-b3 |
9.2-b |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{6} \) |
$14.27074$ |
$(a^3+2a^2-7a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$925.2797820$ |
1.906274461 |
\( -\frac{49603}{81} a^{3} + \frac{195404}{81} a^{2} - \frac{45730}{81} a - \frac{302041}{81} \) |
\( \bigl[1\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{34}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( a^{2} + a - 7\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{34}{3}\right){x}^{2}+\left(a^{2}+a-7\right){x}+\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}$ |
| 9.2-b4 |
9.2-b |
$4$ |
$6$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$14.27074$ |
$(a^3+2a^2-7a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$462.6398910$ |
1.906274461 |
\( \frac{111278780710750}{27} a^{3} - \frac{255161333055218}{27} a^{2} - \frac{1116702686314064}{27} a + \frac{2667954003726349}{27} \) |
\( \bigl[a + 1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{8}{3} a + \frac{8}{3}\) , \( 0\) , \( \frac{4}{3} a^{3} + \frac{4}{3} a^{2} - \frac{44}{3} a - \frac{56}{3}\) , \( \frac{29}{3} a^{3} + \frac{38}{3} a^{2} - \frac{286}{3} a - \frac{370}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{8}{3}a+\frac{8}{3}\right){x}^{2}+\left(\frac{4}{3}a^{3}+\frac{4}{3}a^{2}-\frac{44}{3}a-\frac{56}{3}\right){x}+\frac{29}{3}a^{3}+\frac{38}{3}a^{2}-\frac{286}{3}a-\frac{370}{3}$ |
| 11.1-a1 |
11.1-a |
$2$ |
$2$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$14.63323$ |
$(2/3a^3+2/3a^2-19/3a-10/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$381.7431959$ |
1.572945436 |
\( \frac{864848}{363} a^{3} + \frac{103541}{363} a^{2} - \frac{4706851}{363} a - \frac{3033397}{363} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( a^{2} + a - 5\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{5}{3} a - \frac{23}{3}\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} + \frac{4}{3} a + \frac{16}{3}\) , \( \frac{1}{3} a^{3} - \frac{14}{3} a^{2} + \frac{10}{3} a + \frac{58}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{5}{3}a-\frac{23}{3}\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(\frac{1}{3}a^{3}-\frac{2}{3}a^{2}+\frac{4}{3}a+\frac{16}{3}\right){x}+\frac{1}{3}a^{3}-\frac{14}{3}a^{2}+\frac{10}{3}a+\frac{58}{3}$ |
| 11.1-a2 |
11.1-a |
$2$ |
$2$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{4} \) |
$14.63323$ |
$(2/3a^3+2/3a^2-19/3a-10/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$95.43579897$ |
1.572945436 |
\( -\frac{43074411905}{14641} a^{3} + \frac{2324145080828}{14641} a^{2} - \frac{2770592746793}{14641} a - \frac{7561024713211}{14641} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{8}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{5}{3} a - \frac{23}{3}\) , \( -200 a^{3} - 381 a^{2} + 1480 a + 2117\) , \( -\frac{10378}{3} a^{3} - \frac{19834}{3} a^{2} + \frac{77141}{3} a + \frac{110456}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{5}{3}a-\frac{23}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{8}{3}a+\frac{11}{3}\right){x}^{2}+\left(-200a^{3}-381a^{2}+1480a+2117\right){x}-\frac{10378}{3}a^{3}-\frac{19834}{3}a^{2}+\frac{77141}{3}a+\frac{110456}{3}$ |
| 11.1-b1 |
11.1-b |
$2$ |
$2$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$14.63323$ |
$(2/3a^3+2/3a^2-19/3a-10/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.109806644$ |
$1591.979267$ |
2.881166607 |
\( \frac{864848}{363} a^{3} + \frac{103541}{363} a^{2} - \frac{4706851}{363} a - \frac{3033397}{363} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{31}{3}\) , \( -a^{2} + 7\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{31}{3}\) , \( \frac{14}{3} a^{3} + \frac{20}{3} a^{2} - \frac{109}{3} a - \frac{88}{3}\) , \( \frac{25}{3} a^{3} + \frac{40}{3} a^{2} - \frac{191}{3} a - \frac{203}{3}\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{31}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{31}{3}\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(\frac{14}{3}a^{3}+\frac{20}{3}a^{2}-\frac{109}{3}a-\frac{88}{3}\right){x}+\frac{25}{3}a^{3}+\frac{40}{3}a^{2}-\frac{191}{3}a-\frac{203}{3}$ |
| 11.1-b2 |
11.1-b |
$2$ |
$2$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{4} \) |
$14.63323$ |
$(2/3a^3+2/3a^2-19/3a-10/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.219613289$ |
$397.9948169$ |
2.881166607 |
\( -\frac{43074411905}{14641} a^{3} + \frac{2324145080828}{14641} a^{2} - \frac{2770592746793}{14641} a - \frac{7561024713211}{14641} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{31}{3}\) , \( -a^{2} + 7\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{31}{3}\) , \( \frac{4}{3} a^{3} - \frac{5}{3} a^{2} - \frac{29}{3} a + \frac{37}{3}\) , \( -19 a^{3} - 34 a^{2} + 133 a + 208\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{31}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{31}{3}\right){y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(\frac{4}{3}a^{3}-\frac{5}{3}a^{2}-\frac{29}{3}a+\frac{37}{3}\right){x}-19a^{3}-34a^{2}+133a+208$ |
| 11.2-a1 |
11.2-a |
$2$ |
$2$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$14.63323$ |
$(-4/3a^3-7/3a^2+29/3a+38/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$381.7431959$ |
1.572945436 |
\( \frac{787822}{121} a^{3} + \frac{1041591}{121} a^{2} - \frac{7039887}{121} a - \frac{7315364}{121} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{13}{3} a + \frac{31}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( 4 a^{3} + 6 a^{2} - 34 a - 40\) , \( \frac{10}{3} a^{3} + \frac{16}{3} a^{2} - \frac{92}{3} a - \frac{134}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{13}{3}a+\frac{31}{3}\right){x}^{2}+\left(4a^{3}+6a^{2}-34a-40\right){x}+\frac{10}{3}a^{3}+\frac{16}{3}a^{2}-\frac{92}{3}a-\frac{134}{3}$ |
| 11.2-a2 |
11.2-a |
$2$ |
$2$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{4} \) |
$14.63323$ |
$(-4/3a^3-7/3a^2+29/3a+38/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$95.43579897$ |
1.572945436 |
\( -\frac{3448689918649}{14641} a^{3} - \frac{5815909411382}{14641} a^{2} + \frac{30704707391225}{14641} a + \frac{44975345211504}{14641} \) |
\( \bigl[a + 1\) , \( -a^{2} + 7\) , \( 1\) , \( -\frac{166}{3} a^{3} + \frac{377}{3} a^{2} + \frac{1676}{3} a - \frac{3979}{3}\) , \( -\frac{2978}{3} a^{3} + \frac{6829}{3} a^{2} + \frac{29893}{3} a - \frac{71426}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+7\right){x}^{2}+\left(-\frac{166}{3}a^{3}+\frac{377}{3}a^{2}+\frac{1676}{3}a-\frac{3979}{3}\right){x}-\frac{2978}{3}a^{3}+\frac{6829}{3}a^{2}+\frac{29893}{3}a-\frac{71426}{3}$ |
| 11.2-b1 |
11.2-b |
$2$ |
$2$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( - 11^{4} \) |
$14.63323$ |
$(-4/3a^3-7/3a^2+29/3a+38/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.219613289$ |
$397.9948169$ |
2.881166607 |
\( -\frac{3448689918649}{14641} a^{3} - \frac{5815909411382}{14641} a^{2} + \frac{30704707391225}{14641} a + \frac{44975345211504}{14641} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{13}{3} a + \frac{31}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( 2 a^{2} - 2 a - 29\) , \( -\frac{37}{3} a^{3} + \frac{2}{3} a^{2} + \frac{344}{3} a - \frac{133}{3}\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{13}{3}a+\frac{31}{3}\right){x}^{2}+\left(2a^{2}-2a-29\right){x}-\frac{37}{3}a^{3}+\frac{2}{3}a^{2}+\frac{344}{3}a-\frac{133}{3}$ |
| 11.2-b2 |
11.2-b |
$2$ |
$2$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$14.63323$ |
$(-4/3a^3-7/3a^2+29/3a+38/3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.109806644$ |
$1591.979267$ |
2.881166607 |
\( \frac{787822}{121} a^{3} + \frac{1041591}{121} a^{2} - \frac{7039887}{121} a - \frac{7315364}{121} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{13}{3} a + \frac{31}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( -\frac{5}{3} a^{3} - \frac{14}{3} a^{2} + \frac{34}{3} a + \frac{88}{3}\) , \( -a^{3} - 3 a^{2} + 7 a + 20\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{13}{3}a+\frac{31}{3}\right){x}^{2}+\left(-\frac{5}{3}a^{3}-\frac{14}{3}a^{2}+\frac{34}{3}a+\frac{88}{3}\right){x}-a^{3}-3a^{2}+7a+20$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$15.33491$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Ns.2.1[2] |
$1$ |
\( 1 \) |
$1$ |
$179.8356622$ |
1.481999874 |
\( \frac{2305}{32} a^{3} + \frac{2305}{32} a^{2} - \frac{2305}{4} a - \frac{10497}{32} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{34}{3}\) , \( a^{2} + a - 6\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{26}{3}\) , \( \frac{5}{3} a^{3} + \frac{8}{3} a^{2} - \frac{34}{3} a - \frac{31}{3}\) , \( \frac{4}{3} a^{3} + \frac{19}{3} a^{2} - \frac{20}{3} a - \frac{131}{3}\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{34}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{26}{3}\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(\frac{5}{3}a^{3}+\frac{8}{3}a^{2}-\frac{34}{3}a-\frac{31}{3}\right){x}+\frac{4}{3}a^{3}+\frac{19}{3}a^{2}-\frac{20}{3}a-\frac{131}{3}$ |
| 16.1-b1 |
16.1-b |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.33491$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.230885885$ |
$217.9047343$ |
3.316854235 |
\( \frac{12566365}{12} a^{3} + \frac{4952365}{3} a^{2} - \frac{56165965}{6} a - \frac{151199489}{12} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{19}{3} a + \frac{37}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{31}{3}\) , \( -25 a^{3} + 46 a^{2} + 246 a - 499\) , \( -\frac{2719}{3} a^{3} + \frac{6203}{3} a^{2} + \frac{27269}{3} a - \frac{64912}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{31}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{19}{3}a+\frac{37}{3}\right){x}^{2}+\left(-25a^{3}+46a^{2}+246a-499\right){x}-\frac{2719}{3}a^{3}+\frac{6203}{3}a^{2}+\frac{27269}{3}a-\frac{64912}{3}$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.33491$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.069409818$ |
$754.2875629$ |
3.451597838 |
\( 115800 a^{3} - \frac{1951165}{4} a^{2} + \frac{114035}{2} a + \frac{4443587}{4} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( a^{2} - a - 7\) , \( 0\) , \( -\frac{7}{3} a^{3} - \frac{4}{3} a^{2} + \frac{38}{3} a + \frac{56}{3}\) , \( -11 a^{3} - 17 a^{2} + 77 a + 102\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-\frac{7}{3}a^{3}-\frac{4}{3}a^{2}+\frac{38}{3}a+\frac{56}{3}\right){x}-11a^{3}-17a^{2}+77a+102$ |
| 16.1-d1 |
16.1-d |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.33491$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.230885885$ |
$217.9047343$ |
3.316854235 |
\( 115800 a^{3} - \frac{1951165}{4} a^{2} + \frac{114035}{2} a + \frac{4443587}{4} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{31}{3}\) , \( -82 a^{3} - 156 a^{2} + 610 a + 872\) , \( -\frac{9560}{3} a^{3} - \frac{18269}{3} a^{2} + \frac{71098}{3} a + \frac{101803}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{31}{3}\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-82a^{3}-156a^{2}+610a+872\right){x}-\frac{9560}{3}a^{3}-\frac{18269}{3}a^{2}+\frac{71098}{3}a+\frac{101803}{3}$ |
| 16.1-e1 |
16.1-e |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$15.33491$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.069409818$ |
$754.2875629$ |
3.451597838 |
\( \frac{12566365}{12} a^{3} + \frac{4952365}{3} a^{2} - \frac{56165965}{6} a - \frac{151199489}{12} \) |
\( \bigl[a + 1\) , \( a^{2} + a - 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{5}{3}\) , \( 2 a^{3} + 5 a^{2} - 13 a - 28\) , \( \frac{5}{3} a^{3} + \frac{35}{3} a^{2} - \frac{19}{3} a - \frac{262}{3}\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{5}{3}\right){y}={x}^{3}+\left(a^{2}+a-5\right){x}^{2}+\left(2a^{3}+5a^{2}-13a-28\right){x}+\frac{5}{3}a^{3}+\frac{35}{3}a^{2}-\frac{19}{3}a-\frac{262}{3}$ |
| 16.1-f1 |
16.1-f |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$15.33491$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5Ns.2.1[2] |
$1$ |
\( 1 \) |
$1$ |
$179.8356622$ |
1.481999874 |
\( \frac{2305}{32} a^{3} + \frac{2305}{32} a^{2} - \frac{2305}{4} a - \frac{10497}{32} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{26}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{13}{3} a + \frac{37}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{34}{3}\) , \( \frac{4}{3} a^{3} + \frac{1}{3} a^{2} - \frac{38}{3} a + \frac{19}{3}\) , \( -\frac{7}{3} a^{3} - \frac{22}{3} a^{2} + \frac{44}{3} a + \frac{149}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{26}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{34}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{13}{3}a+\frac{37}{3}\right){x}^{2}+\left(\frac{4}{3}a^{3}+\frac{1}{3}a^{2}-\frac{38}{3}a+\frac{19}{3}\right){x}-\frac{7}{3}a^{3}-\frac{22}{3}a^{2}+\frac{44}{3}a+\frac{149}{3}$ |
| 29.3-a1 |
29.3-a |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$16.51832$ |
$(-1/3a^3-1/3a^2+11/3a+8/3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$170.5396808$ |
2.810786051 |
\( \frac{15220674}{841} a^{3} + \frac{24234468}{841} a^{2} - \frac{135102915}{841} a - \frac{186405299}{841} \) |
\( \bigl[a + 1\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( 0\) , \( 4 a^{3} + 7 a^{2} - 29 a - 37\) , \( 5 a^{3} + 9 a^{2} - 37 a - 49\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){x}^{2}+\left(4a^{3}+7a^{2}-29a-37\right){x}+5a^{3}+9a^{2}-37a-49$ |
| 29.3-b1 |
29.3-b |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
29.3 |
\( 29 \) |
\( 29^{2} \) |
$16.51832$ |
$(-1/3a^3-1/3a^2+11/3a+8/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.023036274$ |
$1750.630173$ |
2.658697931 |
\( \frac{15220674}{841} a^{3} + \frac{24234468}{841} a^{2} - \frac{135102915}{841} a - \frac{186405299}{841} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{34}{3}\) , \( -\frac{1}{3} a^{3} - \frac{4}{3} a^{2} + \frac{8}{3} a + \frac{23}{3}\) , \( a\) , \( \frac{8}{3} a^{3} + \frac{8}{3} a^{2} - \frac{64}{3} a - \frac{31}{3}\) , \( \frac{11}{3} a^{3} + \frac{14}{3} a^{2} - \frac{85}{3} a - \frac{64}{3}\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{34}{3}\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{4}{3}a^{2}+\frac{8}{3}a+\frac{23}{3}\right){x}^{2}+\left(\frac{8}{3}a^{3}+\frac{8}{3}a^{2}-\frac{64}{3}a-\frac{31}{3}\right){x}+\frac{11}{3}a^{3}+\frac{14}{3}a^{2}-\frac{85}{3}a-\frac{64}{3}$ |
| 29.4-a1 |
29.4-a |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{2} \) |
$16.51832$ |
$(-a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$170.5396808$ |
2.810786051 |
\( \frac{1761039}{841} a^{3} - \frac{250095}{29} a^{2} - \frac{750789}{841} a + \frac{16099786}{841} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{8}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{19}{3} a - \frac{31}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( -\frac{1}{3} a^{3} + \frac{8}{3} a^{2} - \frac{4}{3} a - \frac{19}{3}\) , \( -\frac{1}{3} a^{3} + \frac{11}{3} a^{2} - \frac{10}{3} a - \frac{34}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{19}{3}a-\frac{31}{3}\right){x}^{2}+\left(-\frac{1}{3}a^{3}+\frac{8}{3}a^{2}-\frac{4}{3}a-\frac{19}{3}\right){x}-\frac{1}{3}a^{3}+\frac{11}{3}a^{2}-\frac{10}{3}a-\frac{34}{3}$ |
| 29.4-b1 |
29.4-b |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
29.4 |
\( 29 \) |
\( 29^{2} \) |
$16.51832$ |
$(-a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.023036274$ |
$1750.630173$ |
2.658697931 |
\( \frac{1761039}{841} a^{3} - \frac{250095}{29} a^{2} - \frac{750789}{841} a + \frac{16099786}{841} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{31}{3}\) , \( -\frac{1}{3} a^{3} - \frac{4}{3} a^{2} + \frac{5}{3} a + \frac{23}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{5}{3}\) , \( a^{3} - 2 a^{2} - 9 a + 20\) , \( \frac{7}{3} a^{3} + \frac{1}{3} a^{2} - \frac{59}{3} a + \frac{22}{3}\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{31}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{5}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{4}{3}a^{2}+\frac{5}{3}a+\frac{23}{3}\right){x}^{2}+\left(a^{3}-2a^{2}-9a+20\right){x}+\frac{7}{3}a^{3}+\frac{1}{3}a^{2}-\frac{59}{3}a+\frac{22}{3}$ |
| 31.2-a1 |
31.2-a |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{8} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$64$ |
\( 2 \) |
$1$ |
$41.45563388$ |
2.733039417 |
\( \frac{52173459788120}{923521} a^{3} + \frac{52173459788120}{923521} a^{2} - \frac{417387678304960}{923521} a - \frac{5294432962637}{29791} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( -1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( \frac{11}{3} a^{3} + \frac{11}{3} a^{2} - \frac{88}{3} a - \frac{151}{3}\) , \( -\frac{43}{3} a^{3} - \frac{43}{3} a^{2} + \frac{344}{3} a + \frac{374}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){y}={x}^{3}-{x}^{2}+\left(\frac{11}{3}a^{3}+\frac{11}{3}a^{2}-\frac{88}{3}a-\frac{151}{3}\right){x}-\frac{43}{3}a^{3}-\frac{43}{3}a^{2}+\frac{344}{3}a+\frac{374}{3}$ |
| 31.2-a2 |
31.2-a |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$2.590977117$ |
2.733039417 |
\( \frac{61725871986044215714}{2883} a^{3} + \frac{61725871986044215714}{2883} a^{2} - \frac{493806975888353725712}{2883} a - \frac{6263977397174803553}{93} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( -1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( -\frac{134}{3} a^{3} - \frac{134}{3} a^{2} + \frac{1072}{3} a + \frac{649}{3}\) , \( -246 a^{3} - 246 a^{2} + 1968 a + 1204\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){y}={x}^{3}-{x}^{2}+\left(-\frac{134}{3}a^{3}-\frac{134}{3}a^{2}+\frac{1072}{3}a+\frac{649}{3}\right){x}-246a^{3}-246a^{2}+1968a+1204$ |
| 31.2-a3 |
31.2-a |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$165.8225355$ |
2.733039417 |
\( -\frac{6130703730739448}{93} a^{3} - \frac{6130703730739448}{93} a^{2} + \frac{49045629845915584}{93} a + \frac{1948792893147625}{3} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( \frac{17}{3} a^{3} + \frac{17}{3} a^{2} - \frac{136}{3} a - \frac{91}{3}\) , \( -57 a^{3} - 57 a^{2} + 456 a + 191\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){y}={x}^{3}+{x}^{2}+\left(\frac{17}{3}a^{3}+\frac{17}{3}a^{2}-\frac{136}{3}a-\frac{91}{3}\right){x}-57a^{3}-57a^{2}+456a+191$ |
| 31.2-a4 |
31.2-a |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$663.2901421$ |
2.733039417 |
\( -\frac{3009757520}{961} a^{3} - \frac{3009757520}{961} a^{2} + \frac{24078060160}{961} a + \frac{957351303}{31} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{8}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( -\frac{2}{3} a^{3} - \frac{2}{3} a^{2} + \frac{16}{3} a + \frac{1}{3}\) , \( -a^{3} - a^{2} + 8 a + 3\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{8}{3}a+\frac{11}{3}\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{2}{3}a^{2}+\frac{16}{3}a+\frac{1}{3}\right){x}-a^{3}-a^{2}+8a+3$ |
| 31.2-a5 |
31.2-a |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$2653.160568$ |
2.733039417 |
\( \frac{106208}{93} a^{3} + \frac{106208}{93} a^{2} - \frac{849664}{93} a - \frac{22429}{3} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{8}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( -\frac{2}{3} a^{3} - \frac{2}{3} a^{2} + \frac{16}{3} a + \frac{16}{3}\) , \( 0\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{8}{3}a+\frac{11}{3}\right){x}^{2}+\left(-\frac{2}{3}a^{3}-\frac{2}{3}a^{2}+\frac{16}{3}a+\frac{16}{3}\right){x}$ |
| 31.2-a6 |
31.2-a |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{16} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$2.590977117$ |
2.733039417 |
\( -\frac{11889611722383394}{2558673112323} a^{3} - \frac{11889611722383394}{2558673112323} a^{2} + \frac{95116893779067152}{2558673112323} a + \frac{2233185115893809}{82537842333} \) |
\( \bigl[1\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{8}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{8}{3}\) , \( -\frac{32}{3} a^{3} - \frac{32}{3} a^{2} + \frac{256}{3} a + \frac{31}{3}\) , \( -47 a^{3} - 47 a^{2} + 376 a + 73\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{8}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{8}{3}a+\frac{11}{3}\right){x}^{2}+\left(-\frac{32}{3}a^{3}-\frac{32}{3}a^{2}+\frac{256}{3}a+\frac{31}{3}\right){x}-47a^{3}-47a^{2}+376a+73$ |
| 31.2-b1 |
31.2-b |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.103585138$ |
$585.4101683$ |
3.997790662 |
\( \frac{8125}{93} a^{3} + \frac{8125}{93} a^{2} - \frac{65000}{93} a - \frac{1250}{3} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{5}{3} a - \frac{23}{3}\) , \( a^{2} - a - 7\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{26}{3}\) , \( 3 a^{3} + 8 a^{2} - 23 a - 44\) , \( \frac{19}{3} a^{3} + \frac{40}{3} a^{2} - \frac{143}{3} a - \frac{221}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{5}{3}a-\frac{23}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{26}{3}\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(3a^{3}+8a^{2}-23a-44\right){x}+\frac{19}{3}a^{3}+\frac{40}{3}a^{2}-\frac{143}{3}a-\frac{221}{3}$ |
| 31.2-c1 |
31.2-c |
$1$ |
$1$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.103585138$ |
$585.4101683$ |
3.997790662 |
\( \frac{8125}{93} a^{3} + \frac{8125}{93} a^{2} - \frac{65000}{93} a - \frac{1250}{3} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{5}{3} a - \frac{26}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{29}{3}\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{8}{3} a - \frac{5}{3}\) , \( \frac{13}{3} a^{3} + \frac{22}{3} a^{2} - \frac{98}{3} a - \frac{113}{3}\) , \( 6 a^{3} + 11 a^{2} - 45 a - 60\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{5}{3}a-\frac{26}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{8}{3}a-\frac{5}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{29}{3}\right){x}^{2}+\left(\frac{13}{3}a^{3}+\frac{22}{3}a^{2}-\frac{98}{3}a-\frac{113}{3}\right){x}+6a^{3}+11a^{2}-45a-60$ |
| 31.2-d1 |
31.2-d |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$13.54712246$ |
$5.756461161$ |
5.141205589 |
\( -\frac{6130703730739448}{93} a^{3} - \frac{6130703730739448}{93} a^{2} + \frac{49045629845915584}{93} a + \frac{1948792893147625}{3} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{31}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{23}{3}\) , \( 1\) , \( 169 a^{3} + 315 a^{2} - 1294 a - 1832\) , \( -14461 a^{3} - 27679 a^{2} + 107348 a + 153813\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{31}{3}\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{23}{3}\right){x}^{2}+\left(169a^{3}+315a^{2}-1294a-1832\right){x}-14461a^{3}-27679a^{2}+107348a+153813$ |
| 31.2-d2 |
31.2-d |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{8} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$13.54712246$ |
$23.02584464$ |
5.141205589 |
\( \frac{52173459788120}{923521} a^{3} + \frac{52173459788120}{923521} a^{2} - \frac{417387678304960}{923521} a - \frac{5294432962637}{29791} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{31}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{11}{3} a - \frac{23}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{5}{3} a - \frac{26}{3}\) , \( 3 a^{3} - 17 a^{2} - 136 a - 149\) , \( -\frac{2024}{3} a^{3} - \frac{4373}{3} a^{2} + \frac{12766}{3} a + \frac{19423}{3}\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{31}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{5}{3}a-\frac{26}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{11}{3}a-\frac{23}{3}\right){x}^{2}+\left(3a^{3}-17a^{2}-136a-149\right){x}-\frac{2024}{3}a^{3}-\frac{4373}{3}a^{2}+\frac{12766}{3}a+\frac{19423}{3}$ |
| 31.2-d3 |
31.2-d |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$54.18848987$ |
$1.439115290$ |
5.141205589 |
\( \frac{61725871986044215714}{2883} a^{3} + \frac{61725871986044215714}{2883} a^{2} - \frac{493806975888353725712}{2883} a - \frac{6263977397174803553}{93} \) |
\( \bigl[\frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{13}{3} a - \frac{31}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{11}{3} a - \frac{23}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{5}{3} a - \frac{26}{3}\) , \( -\frac{4211}{3} a^{3} - \frac{7886}{3} a^{2} + \frac{31987}{3} a + \frac{45403}{3}\) , \( -\frac{160549}{3} a^{3} - \frac{310228}{3} a^{2} + \frac{1178621}{3} a + \frac{1695506}{3}\bigr] \) |
${y}^2+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{13}{3}a-\frac{31}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{5}{3}a-\frac{26}{3}\right){y}={x}^{3}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{11}{3}a-\frac{23}{3}\right){x}^{2}+\left(-\frac{4211}{3}a^{3}-\frac{7886}{3}a^{2}+\frac{31987}{3}a+\frac{45403}{3}\right){x}-\frac{160549}{3}a^{3}-\frac{310228}{3}a^{2}+\frac{1178621}{3}a+\frac{1695506}{3}$ |
| 31.2-d4 |
31.2-d |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{2} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.846695154$ |
$368.4135143$ |
5.141205589 |
\( \frac{106208}{93} a^{3} + \frac{106208}{93} a^{2} - \frac{849664}{93} a - \frac{22429}{3} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{5}{3}\) , \( a^{2} + a - 6\) , \( a + 1\) , \( \frac{5}{3} a^{3} + \frac{26}{3} a^{2} - \frac{25}{3} a - \frac{187}{3}\) , \( 11 a^{3} - 6 a^{2} - 97 a + 101\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{5}{3}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(\frac{5}{3}a^{3}+\frac{26}{3}a^{2}-\frac{25}{3}a-\frac{187}{3}\right){x}+11a^{3}-6a^{2}-97a+101$ |
| 31.2-d5 |
31.2-d |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{4} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$3.386780617$ |
$92.10337857$ |
5.141205589 |
\( -\frac{3009757520}{961} a^{3} - \frac{3009757520}{961} a^{2} + \frac{24078060160}{961} a + \frac{957351303}{31} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - \frac{5}{3} a - \frac{5}{3}\) , \( a^{2} + a - 6\) , \( a + 1\) , \( -5 a^{3} + 22 a^{2} + 70 a - 239\) , \( -\frac{95}{3} a^{3} + \frac{244}{3} a^{2} + \frac{1168}{3} a - \frac{3008}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{1}{3}a^{2}-\frac{5}{3}a-\frac{5}{3}\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}+a-6\right){x}^{2}+\left(-5a^{3}+22a^{2}+70a-239\right){x}-\frac{95}{3}a^{3}+\frac{244}{3}a^{2}+\frac{1168}{3}a-\frac{3008}{3}$ |
| 31.2-d6 |
31.2-d |
$6$ |
$8$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
31.2 |
\( 31 \) |
\( 31^{16} \) |
$16.65660$ |
$(1/3a^3+1/3a^2-5/3a-17/3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$13.54712246$ |
$5.756461161$ |
5.141205589 |
\( -\frac{11889611722383394}{2558673112323} a^{3} - \frac{11889611722383394}{2558673112323} a^{2} + \frac{95116893779067152}{2558673112323} a + \frac{2233185115893809}{82537842333} \) |
\( \bigl[a\) , \( a^{2} - a - 7\) , \( a + 1\) , \( -\frac{1442}{3} a^{3} - \frac{2804}{3} a^{2} + \frac{10477}{3} a + \frac{15124}{3}\) , \( -\frac{45004}{3} a^{3} - \frac{85603}{3} a^{2} + \frac{336458}{3} a + \frac{480866}{3}\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-\frac{1442}{3}a^{3}-\frac{2804}{3}a^{2}+\frac{10477}{3}a+\frac{15124}{3}\right){x}-\frac{45004}{3}a^{3}-\frac{85603}{3}a^{2}+\frac{336458}{3}a+\frac{480866}{3}$ |
| 41.1-a1 |
41.1-a |
$4$ |
$4$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$17.24901$ |
$(1/3a^3+4/3a^2-8/3a-20/3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$8.923202449$ |
3.959644299 |
\( -\frac{524435210383946556123}{1681} a^{3} - \frac{827258307850571456586}{1681} a^{2} + \frac{4685459762682423412619}{1681} a + \frac{6307643611345628685496}{1681} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{26}{3}\) , \( -\frac{2}{3} a^{3} - \frac{5}{3} a^{2} + \frac{13}{3} a + \frac{34}{3}\) , \( \frac{2}{3} a^{3} + \frac{5}{3} a^{2} - \frac{16}{3} a - \frac{34}{3}\) , \( -\frac{10}{3} a^{3} - \frac{412}{3} a^{2} + \frac{560}{3} a + \frac{1460}{3}\) , \( 171 a^{3} - 1375 a^{2} + 912 a + 3854\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{26}{3}\right){x}{y}+\left(\frac{2}{3}a^{3}+\frac{5}{3}a^{2}-\frac{16}{3}a-\frac{34}{3}\right){y}={x}^{3}+\left(-\frac{2}{3}a^{3}-\frac{5}{3}a^{2}+\frac{13}{3}a+\frac{34}{3}\right){x}^{2}+\left(-\frac{10}{3}a^{3}-\frac{412}{3}a^{2}+\frac{560}{3}a+\frac{1460}{3}\right){x}+171a^{3}-1375a^{2}+912a+3854$ |
| 41.1-a2 |
41.1-a |
$4$ |
$4$ |
4.4.14725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{8} \) |
$17.24901$ |
$(1/3a^3+4/3a^2-8/3a-20/3)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2^{3} \) |
$1$ |
$35.69280979$ |
3.959644299 |
\( \frac{27421182445191955009}{23954775687363} a^{3} + \frac{22298823014844571006}{23954775687363} a^{2} - \frac{745518480589422222161}{23954775687363} a + \frac{1304828386288051184584}{23954775687363} \) |
\( \bigl[\frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{23}{3}\) , \( -\frac{1}{3} a^{3} - \frac{1}{3} a^{2} + \frac{11}{3} a + \frac{11}{3}\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - \frac{8}{3} a - \frac{26}{3}\) , \( \frac{491}{3} a^{3} + \frac{812}{3} a^{2} - \frac{4369}{3} a - \frac{6241}{3}\) , \( \frac{7466}{3} a^{3} + \frac{11921}{3} a^{2} - \frac{66658}{3} a - \frac{91126}{3}\bigr] \) |
${y}^2+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{23}{3}\right){x}{y}+\left(\frac{1}{3}a^{3}+\frac{4}{3}a^{2}-\frac{8}{3}a-\frac{26}{3}\right){y}={x}^{3}+\left(-\frac{1}{3}a^{3}-\frac{1}{3}a^{2}+\frac{11}{3}a+\frac{11}{3}\right){x}^{2}+\left(\frac{491}{3}a^{3}+\frac{812}{3}a^{2}-\frac{4369}{3}a-\frac{6241}{3}\right){x}+\frac{7466}{3}a^{3}+\frac{11921}{3}a^{2}-\frac{66658}{3}a-\frac{91126}{3}$ |
*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.
