| 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 |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$123.88401$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2B, 5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$7822.609539$ |
1.41064 |
\( -59094646784 a^{5} + 83036741536 a^{4} + 439115129056 a^{3} - 118812483232 a^{2} - 660999651584 a - 145858637200 \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 5\) , \( -2 a^{5} + 3 a^{4} + 15 a^{3} - 6 a^{2} - 23 a - 2\) , \( a^{2} - a - 2\) , \( -17 a^{5} + 29 a^{4} + 125 a^{3} - 69 a^{2} - 223 a - 43\) , \( -25 a^{5} + 36 a^{4} + 184 a^{3} - 53 a^{2} - 275 a - 58\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+5\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+15a^{3}-6a^{2}-23a-2\right){x}^{2}+\left(-17a^{5}+29a^{4}+125a^{3}-69a^{2}-223a-43\right){x}-25a^{5}+36a^{4}+184a^{3}-53a^{2}-275a-58$ |
| 1.1-a2 |
1.1-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$123.88401$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2B, 5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$7822.609539$ |
1.41064 |
\( -7398982016 a^{5} + 19837518400 a^{4} + 25842912000 a^{3} - 36046349280 a^{2} - 28190257440 a - 4401008816 \) |
\( \bigl[5 a^{5} - 7 a^{4} - 37 a^{3} + 10 a^{2} + 54 a + 14\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 3 a + 5\) , \( 3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 7\) , \( 66 a^{5} - 90 a^{4} - 499 a^{3} + 126 a^{2} + 757 a + 167\) , \( 175 a^{5} - 243 a^{4} - 1309 a^{3} + 344 a^{2} + 1975 a + 436\bigr] \) |
${y}^2+\left(5a^{5}-7a^{4}-37a^{3}+10a^{2}+54a+14\right){x}{y}+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+7\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+3a+5\right){x}^{2}+\left(66a^{5}-90a^{4}-499a^{3}+126a^{2}+757a+167\right){x}+175a^{5}-243a^{4}-1309a^{3}+344a^{2}+1975a+436$ |
| 1.1-a3 |
1.1-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$123.88401$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
✓ |
$2, 5$ |
2Cs, 5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$31290.43815$ |
1.41064 |
\( -245760 a^{5} + 368640 a^{4} + 1720320 a^{3} - 491520 a^{2} - 2457600 a - 536576 \) |
\( \bigl[0\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 8 a^{2} + 1\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 7\) , \( 2 a^{5} - 4 a^{4} - 10 a^{3} + 7 a^{2} + 4 a - 1\) , \( 2 a^{5} - 2 a^{4} - 14 a^{3} - 3 a^{2} + 11 a + 2\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+7\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-8a^{2}+1\right){x}^{2}+\left(2a^{5}-4a^{4}-10a^{3}+7a^{2}+4a-1\right){x}+2a^{5}-2a^{4}-14a^{3}-3a^{2}+11a+2$ |
| 1.1-a4 |
1.1-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$123.88401$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 5$ |
2B, 5Nn.2.2[2] |
$1$ |
\( 1 \) |
$1$ |
$7822.609539$ |
1.41064 |
\( -1591721600 a^{5} - 746234336 a^{4} + 11639411744 a^{3} + 18688131712 a^{2} + 8336405024 a + 1086699280 \) |
\( \bigl[5 a^{5} - 7 a^{4} - 37 a^{3} + 10 a^{2} + 54 a + 14\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 4 a + 3\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 2\) , \( -a^{5} + 4 a^{4} + 26 a^{3} - 6 a^{2} - 48 a - 8\) , \( -2 a^{5} - 9 a^{4} + 11 a^{3} + 18 a^{2} - 12 a - 3\bigr] \) |
${y}^2+\left(5a^{5}-7a^{4}-37a^{3}+10a^{2}+54a+14\right){x}{y}+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-9a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+4a+3\right){x}^{2}+\left(-a^{5}+4a^{4}+26a^{3}-6a^{2}-48a-8\right){x}-2a^{5}-9a^{4}+11a^{3}+18a^{2}-12a-3$ |
| 11.1-a1 |
11.1-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( -\frac{567083889325376}{214358881} a^{5} + \frac{1513313150167328}{214358881} a^{4} + \frac{2003080636514880}{214358881} a^{3} - \frac{2747045266707680}{214358881} a^{2} - \frac{2202635343341760}{214358881} a - \frac{347517168900976}{214358881} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 5\) , \( -2 a^{5} + 2 a^{4} + 17 a^{3} - 30 a - 8\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 5 a^{2} + 8 a + 1\) , \( -11 a^{5} + 17 a^{4} + 79 a^{3} - 25 a^{2} - 135 a - 30\) , \( -1332 a^{5} + 3080 a^{4} + 6618 a^{3} - 7337 a^{2} - 6406 a - 1034\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+5\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+5a^{2}+8a+1\right){y}={x}^{3}+\left(-2a^{5}+2a^{4}+17a^{3}-30a-8\right){x}^{2}+\left(-11a^{5}+17a^{4}+79a^{3}-25a^{2}-135a-30\right){x}-1332a^{5}+3080a^{4}+6618a^{3}-7337a^{2}-6406a-1034$ |
| 11.1-a2 |
11.1-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$32196.47394$ |
2.90297 |
\( \frac{11369979904}{14641} a^{5} - \frac{16341745664}{14641} a^{4} - \frac{87620870144}{14641} a^{3} + \frac{25664552960}{14641} a^{2} + \frac{153698050048}{14641} a + \frac{52835508224}{14641} \) |
\( \bigl[0\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 4 a - 4\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 6\) , \( 4 a^{5} - a^{4} - 29 a^{3} - 28 a^{2} + a + 4\) , \( 16 a^{5} + 2 a^{4} - 114 a^{3} - 153 a^{2} - 52 a - 6\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+6\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-4a-4\right){x}^{2}+\left(4a^{5}-a^{4}-29a^{3}-28a^{2}+a+4\right){x}+16a^{5}+2a^{4}-114a^{3}-153a^{2}-52a-6$ |
| 11.1-a3 |
11.1-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( -\frac{39895247368800}{121} a^{5} - \frac{18678958094976}{121} a^{4} + \frac{291736362818976}{121} a^{3} + \frac{468222532458816}{121} a^{2} + \frac{208709989632480}{121} a + \frac{27171554647408}{121} \) |
\( \bigl[a^{5} - a^{4} - 8 a^{3} + 12 a + 5\) , \( 5 a^{5} - 7 a^{4} - 37 a^{3} + 9 a^{2} + 56 a + 14\) , \( 1\) , \( -7 a^{5} + 13 a^{4} + 42 a^{3} - 30 a^{2} - 69 a - 13\) , \( -2 a^{5} - 3 a^{4} - 24 a^{3} - 12 a^{2} + 30 a + 8\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-8a^{3}+12a+5\right){x}{y}+{y}={x}^{3}+\left(5a^{5}-7a^{4}-37a^{3}+9a^{2}+56a+14\right){x}^{2}+\left(-7a^{5}+13a^{4}+42a^{3}-30a^{2}-69a-13\right){x}-2a^{5}-3a^{4}-24a^{3}-12a^{2}+30a+8$ |
| 11.1-a4 |
11.1-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( \frac{130785490380192}{121} a^{5} - \frac{162207961106848}{121} a^{4} - \frac{1007225392535008}{121} a^{3} + \frac{110989072806048}{121} a^{2} + \frac{1542383992271072}{121} a + \frac{545493154360016}{121} \) |
\( \bigl[4 a^{5} - 5 a^{4} - 31 a^{3} + 6 a^{2} + 45 a + 11\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 6 a + 1\) , \( 3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 7\) , \( -193 a^{5} + 290 a^{4} + 1380 a^{3} - 449 a^{2} - 2032 a - 445\) , \( -1010 a^{5} + 1459 a^{4} + 7393 a^{3} - 2168 a^{2} - 11028 a - 2422\bigr] \) |
${y}^2+\left(4a^{5}-5a^{4}-31a^{3}+6a^{2}+45a+11\right){x}{y}+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+7\right){y}={x}^{3}+\left(a^{4}-3a^{3}-3a^{2}+6a+1\right){x}^{2}+\left(-193a^{5}+290a^{4}+1380a^{3}-449a^{2}-2032a-445\right){x}-1010a^{5}+1459a^{4}+7393a^{3}-2168a^{2}-11028a-2422$ |
| 11.1-b1 |
11.1-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.085148820$ |
$34026.71633$ |
3.13483 |
\( \frac{481240701344}{11} a^{5} + \frac{1045665237376}{11} a^{4} - \frac{532185240128}{11} a^{3} - \frac{2169787837856}{11} a^{2} - \frac{1109526185088}{11} a - \frac{151674667696}{11} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 5\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 10 a - 2\) , \( a^{5} - a^{4} - 8 a^{3} + 12 a + 4\) , \( -6 a^{5} + 13 a^{4} + 30 a^{3} - 25 a^{2} - 38 a - 1\) , \( -16 a^{5} + 26 a^{4} + 106 a^{3} - 34 a^{2} - 156 a - 46\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+5\right){x}{y}+\left(a^{5}-a^{4}-8a^{3}+12a+4\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-10a-2\right){x}^{2}+\left(-6a^{5}+13a^{4}+30a^{3}-25a^{2}-38a-1\right){x}-16a^{5}+26a^{4}+106a^{3}-34a^{2}-156a-46$ |
| 11.1-b2 |
11.1-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.085148820$ |
$34026.71633$ |
3.13483 |
\( -\frac{356032288}{11} a^{5} + \frac{541392576}{11} a^{4} + \frac{2561432800}{11} a^{3} - \frac{1002315104}{11} a^{2} - \frac{3709730176}{11} a - \frac{338857616}{11} \) |
\( \bigl[a^{5} - a^{4} - 8 a^{3} + 12 a + 5\) , \( -3 a^{5} + 3 a^{4} + 25 a^{3} - a^{2} - 38 a - 11\) , \( a^{5} - a^{4} - 8 a^{3} + 12 a + 4\) , \( -2 a^{5} + 6 a^{4} + 11 a^{3} - 28 a^{2} - 44 a - 10\) , \( -5 a^{5} - 3 a^{4} + 38 a^{3} + 56 a^{2} + 17 a + 1\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-8a^{3}+12a+5\right){x}{y}+\left(a^{5}-a^{4}-8a^{3}+12a+4\right){y}={x}^{3}+\left(-3a^{5}+3a^{4}+25a^{3}-a^{2}-38a-11\right){x}^{2}+\left(-2a^{5}+6a^{4}+11a^{3}-28a^{2}-44a-10\right){x}-5a^{5}-3a^{4}+38a^{3}+56a^{2}+17a+1$ |
| 11.1-b3 |
11.1-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.042574410$ |
$136106.8653$ |
3.13483 |
\( \frac{942080}{121} a^{5} + \frac{2940928}{121} a^{4} + \frac{503808}{121} a^{3} - \frac{6049792}{121} a^{2} - \frac{5386240}{121} a - \frac{69632}{121} \) |
\( \bigl[0\) , \( 3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 28 a + 6\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 5 a^{2} + 8 a + 1\) , \( 20 a^{5} - 29 a^{4} - 147 a^{3} + 47 a^{2} + 220 a + 39\) , \( -90 a^{5} + 126 a^{4} + 669 a^{3} - 176 a^{2} - 1007 a - 232\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+5a^{2}+8a+1\right){y}={x}^{3}+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+28a+6\right){x}^{2}+\left(20a^{5}-29a^{4}-147a^{3}+47a^{2}+220a+39\right){x}-90a^{5}+126a^{4}+669a^{3}-176a^{2}-1007a-232$ |
| 11.1-b4 |
11.1-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.021287205$ |
$34026.71633$ |
3.13483 |
\( \frac{30354790528}{14641} a^{5} - \frac{68301071552}{14641} a^{4} - \frac{158208114144}{14641} a^{3} + \frac{170468651264}{14641} a^{2} + \frac{149487183360}{14641} a + \frac{24235532176}{14641} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 5 a^{2} + 8 a\) , \( 3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 28 a + 6\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 21 a + 7\) , \( -8 a^{5} + 9 a^{4} + 65 a^{3} - 4 a^{2} - 105 a - 37\) , \( 11 a^{5} - 14 a^{4} - 83 a^{3} + 10 a^{2} + 123 a + 43\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+5a^{2}+8a\right){x}{y}+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+21a+7\right){y}={x}^{3}+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+28a+6\right){x}^{2}+\left(-8a^{5}+9a^{4}+65a^{3}-4a^{2}-105a-37\right){x}+11a^{5}-14a^{4}-83a^{3}+10a^{2}+123a+43$ |
| 11.1-c1 |
11.1-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.078422328$ |
$36004.48409$ |
3.05500 |
\( -\frac{12452035648}{11} a^{5} + \frac{17454962912}{11} a^{4} + \frac{92648014816}{11} a^{3} - \frac{24870726784}{11} a^{2} - \frac{139594015136}{11} a - \frac{30816893584}{11} \) |
\( \bigl[3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 6\) , \( 2 a^{5} - 5 a^{4} - 9 a^{3} + 12 a^{2} + 9 a\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 5 a^{2} + 18 a + 4\) , \( 31 a^{5} - 9 a^{4} - 209 a^{3} - 214 a^{2} - 69 a - 9\) , \( -112 a^{5} - 91 a^{4} + 851 a^{3} + 1553 a^{2} + 731 a + 98\bigr] \) |
${y}^2+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+6\right){x}{y}+\left(2a^{5}-3a^{4}-14a^{3}+5a^{2}+18a+4\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-9a^{3}+12a^{2}+9a\right){x}^{2}+\left(31a^{5}-9a^{4}-209a^{3}-214a^{2}-69a-9\right){x}-112a^{5}-91a^{4}+851a^{3}+1553a^{2}+731a+98$ |
| 11.1-c2 |
11.1-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.039211164$ |
$144017.9363$ |
3.05500 |
\( -\frac{5423104}{121} a^{5} - \frac{806912}{121} a^{4} + \frac{39231488}{121} a^{3} + \frac{50819072}{121} a^{2} + \frac{17473536}{121} a + \frac{6029312}{121} \) |
\( \bigl[0\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 19 a + 6\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 2\) , \( 3 a^{5} - 3 a^{4} - 19 a^{3} - 8 a^{2} + 7 a + 3\) , \( -4 a^{5} - 3 a^{4} + 30 a^{3} + 54 a^{2} + 27 a + 4\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-9a-2\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+19a+6\right){x}^{2}+\left(3a^{5}-3a^{4}-19a^{3}-8a^{2}+7a+3\right){x}-4a^{5}-3a^{4}+30a^{3}+54a^{2}+27a+4$ |
| 11.1-c3 |
11.1-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.019605582$ |
$36004.48409$ |
3.05500 |
\( \frac{11413479810944}{14641} a^{5} - \frac{14148506586880}{14641} a^{4} - \frac{87917612487808}{14641} a^{3} + \frac{9654938432288}{14641} a^{2} + \frac{134648691814176}{14641} a + \frac{47627160030352}{14641} \) |
\( \bigl[a^{5} - 11 a^{3} - 3 a^{2} + 18 a + 5\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 21 a + 7\) , \( 4 a^{5} - 5 a^{4} - 31 a^{3} + 5 a^{2} + 48 a + 13\) , \( 5 a^{5} - 7 a^{4} - 38 a^{3} + 11 a^{2} + 59 a + 14\) , \( 3 a^{5} - 6 a^{4} - 19 a^{3} + 11 a^{2} + 28 a + 5\bigr] \) |
${y}^2+\left(a^{5}-11a^{3}-3a^{2}+18a+5\right){x}{y}+\left(4a^{5}-5a^{4}-31a^{3}+5a^{2}+48a+13\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+21a+7\right){x}^{2}+\left(5a^{5}-7a^{4}-38a^{3}+11a^{2}+59a+14\right){x}+3a^{5}-6a^{4}-19a^{3}+11a^{2}+28a+5$ |
| 11.1-c4 |
11.1-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(4a^5-5a^4-31a^3+5a^2+47a+12)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.078422328$ |
$36004.48409$ |
3.05500 |
\( -\frac{792484216384}{11} a^{5} - \frac{371048866784}{11} a^{4} + \frac{5795081180576}{11} a^{3} + \frac{9300897377312}{11} a^{2} + \frac{4145936698688}{11} a + \frac{539758135888}{11} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 5\) , \( -a^{5} + a^{4} + 8 a^{3} - 11 a - 4\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 5 a^{2} + 18 a + 4\) , \( -a^{5} + a^{4} + 10 a^{3} - a^{2} - 16 a - 3\) , \( -2 a^{5} + 5 a^{4} + 16 a^{3} - 10 a^{2} - 24 a - 5\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+5\right){x}{y}+\left(2a^{5}-3a^{4}-14a^{3}+5a^{2}+18a+4\right){y}={x}^{3}+\left(-a^{5}+a^{4}+8a^{3}-11a-4\right){x}^{2}+\left(-a^{5}+a^{4}+10a^{3}-a^{2}-16a-3\right){x}-2a^{5}+5a^{4}+16a^{3}-10a^{2}-24a-5$ |
| 11.2-a1 |
11.2-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( -\frac{185386000382688}{121} a^{5} + \frac{497038180980768}{121} a^{4} + \frac{647517640054752}{121} a^{3} - \frac{903155050715040}{121} a^{2} - \frac{706338657238560}{121} a - \frac{110276659738928}{121} \) |
\( \bigl[-a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 1\) , \( 2 a^{5} - 5 a^{4} - 9 a^{3} + 12 a^{2} + 9 a + 1\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 6\) , \( a^{5} - 8 a^{4} + 8 a^{3} + 23 a^{2} - 24 a - 8\) , \( 5 a^{5} - 7 a^{4} - 19 a^{3} + 15 a^{2} + 16 a + 3\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-9a-1\right){x}{y}+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+6\right){y}={x}^{3}+\left(2a^{5}-5a^{4}-9a^{3}+12a^{2}+9a+1\right){x}^{2}+\left(a^{5}-8a^{4}+8a^{3}+23a^{2}-24a-8\right){x}+5a^{5}-7a^{4}-19a^{3}+15a^{2}+16a+3$ |
| 11.2-a2 |
11.2-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( 11^{8} \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( -\frac{4481945435108320}{214358881} a^{5} + \frac{6295547156760256}{214358881} a^{4} + \frac{33309342533772896}{214358881} a^{3} - \frac{9001480427029696}{214358881} a^{2} - \frac{50143666555771104}{214358881} a - \frac{11065574205267280}{214358881} \) |
\( \bigl[a^{2} - a - 1\) , \( -2 a^{5} + 3 a^{4} + 14 a^{3} - 3 a^{2} - 21 a - 8\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 6\) , \( 4 a^{5} - a^{4} - 33 a^{3} - 20 a^{2} + 28 a + 11\) , \( -82 a^{5} + 109 a^{4} + 636 a^{3} - 123 a^{2} - 1051 a - 369\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+6\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+14a^{3}-3a^{2}-21a-8\right){x}^{2}+\left(4a^{5}-a^{4}-33a^{3}-20a^{2}+28a+11\right){x}-82a^{5}+109a^{4}+636a^{3}-123a^{2}-1051a-369$ |
| 11.2-a3 |
11.2-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$32196.47394$ |
2.90297 |
\( -\frac{5148237824}{14641} a^{5} + \frac{14668865536}{14641} a^{4} + \frac{16139460608}{14641} a^{3} - \frac{27355406336}{14641} a^{2} - \frac{16180191232}{14641} a - \frac{1355743232}{14641} \) |
\( \bigl[0\) , \( a^{5} - a^{4} - 9 a^{3} + a^{2} + 17 a + 4\) , \( 1\) , \( 2 a^{5} - 7 a^{4} - 3 a^{3} + 15 a^{2} - 1\) , \( 5 a^{5} - 13 a^{4} - 18 a^{3} + 23 a^{2} + 20 a + 3\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{5}-a^{4}-9a^{3}+a^{2}+17a+4\right){x}^{2}+\left(2a^{5}-7a^{4}-3a^{3}+15a^{2}-1\right){x}+5a^{5}-13a^{4}-18a^{3}+23a^{2}+20a+3$ |
| 11.2-a4 |
11.2-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( \frac{654972373952}{121} a^{5} + \frac{659198099232}{121} a^{4} - \frac{2201203005248}{121} a^{3} - \frac{1754335064480}{121} a^{2} + \frac{1647145921536}{121} a + \frac{798312050768}{121} \) |
\( \bigl[-a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 1\) , \( -a^{2} + 2 a + 1\) , \( a^{2} - a - 2\) , \( 18 a^{5} - 44 a^{4} - 86 a^{3} + 111 a^{2} + 88 a + 14\) , \( -64 a^{5} + 144 a^{4} + 321 a^{3} - 328 a^{2} - 291 a - 48\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-9a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(18a^{5}-44a^{4}-86a^{3}+111a^{2}+88a+14\right){x}-64a^{5}+144a^{4}+321a^{3}-328a^{2}-291a-48$ |
| 11.2-b1 |
11.2-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.085148820$ |
$34026.71633$ |
3.13483 |
\( -\frac{40634464}{11} a^{5} + \frac{58199232}{11} a^{4} + \frac{211550656}{11} a^{3} + \frac{86537344}{11} a^{2} + \frac{305120}{11} a - \frac{2012432}{11} \) |
\( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 5 a^{2} + 8 a\) , \( a^{4} - 3 a^{3} - 4 a^{2} + 8 a + 3\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 21 a + 7\) , \( -32 a^{5} + 40 a^{4} + 247 a^{3} - 33 a^{2} - 379 a - 122\) , \( -66 a^{5} + 81 a^{4} + 509 a^{3} - 49 a^{2} - 780 a - 287\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-6a^{3}+5a^{2}+8a\right){x}{y}+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+21a+7\right){y}={x}^{3}+\left(a^{4}-3a^{3}-4a^{2}+8a+3\right){x}^{2}+\left(-32a^{5}+40a^{4}+247a^{3}-33a^{2}-379a-122\right){x}-66a^{5}+81a^{4}+509a^{3}-49a^{2}-780a-287$ |
| 11.2-b2 |
11.2-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.042574410$ |
$136106.8653$ |
3.13483 |
\( \frac{120459264}{121} a^{5} - \frac{278798336}{121} a^{4} - \frac{597192704}{121} a^{3} + \frac{664358912}{121} a^{2} + \frac{572456960}{121} a + \frac{92323840}{121} \) |
\( \bigl[0\) , \( -2 a^{5} + 3 a^{4} + 14 a^{3} - 4 a^{2} - 21 a - 6\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 21 a + 7\) , \( -2 a^{5} + 4 a^{4} + 15 a^{3} - 12 a^{2} - 35 a - 11\) , \( -3 a^{4} - a^{3} + 22 a^{2} + 31 a + 9\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+21a+7\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+14a^{3}-4a^{2}-21a-6\right){x}^{2}+\left(-2a^{5}+4a^{4}+15a^{3}-12a^{2}-35a-11\right){x}-3a^{4}-a^{3}+22a^{2}+31a+9$ |
| 11.2-b3 |
11.2-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.021287205$ |
$34026.71633$ |
3.13483 |
\( \frac{64691971104}{14641} a^{5} - \frac{73321064864}{14641} a^{4} - \frac{509656529600}{14641} a^{3} + \frac{6481788288}{14641} a^{2} + \frac{788654130944}{14641} a + \frac{340509101200}{14641} \) |
\( \bigl[2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 21 a + 6\) , \( -a^{5} + a^{4} + 8 a^{3} - 10 a - 4\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 2\) , \( a^{5} - 2 a^{4} - 7 a^{3} + 5 a^{2} + 13 a + 3\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 4 a^{2} + 9 a + 2\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+21a+6\right){x}{y}+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-9a-2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+8a^{3}-10a-4\right){x}^{2}+\left(a^{5}-2a^{4}-7a^{3}+5a^{2}+13a+3\right){x}+a^{5}-2a^{4}-6a^{3}+4a^{2}+9a+2$ |
| 11.2-b4 |
11.2-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.085148820$ |
$34026.71633$ |
3.13483 |
\( \frac{48771008494848}{11} a^{5} - \frac{112913363672288}{11} a^{4} - \frac{241667364611968}{11} a^{3} + \frac{269063591345920}{11} a^{2} + \frac{231386702707488}{11} a + \frac{37083316339920}{11} \) |
\( \bigl[a^{5} - 11 a^{3} - 3 a^{2} + 18 a + 5\) , \( a^{4} - 3 a^{3} - 4 a^{2} + 9 a + 3\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 4 a^{2} + 21 a + 7\) , \( 29 a^{5} - 38 a^{4} - 223 a^{3} + 46 a^{2} + 343 a + 93\) , \( -9 a^{5} + 15 a^{4} + 64 a^{3} - 39 a^{2} - 96 a + 18\bigr] \) |
${y}^2+\left(a^{5}-11a^{3}-3a^{2}+18a+5\right){x}{y}+\left(2a^{5}-3a^{4}-14a^{3}+4a^{2}+21a+7\right){y}={x}^{3}+\left(a^{4}-3a^{3}-4a^{2}+9a+3\right){x}^{2}+\left(29a^{5}-38a^{4}-223a^{3}+46a^{2}+343a+93\right){x}-9a^{5}+15a^{4}+64a^{3}-39a^{2}-96a+18$ |
| 11.2-c1 |
11.2-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.078422328$ |
$36004.48409$ |
3.05500 |
\( -\frac{3682567995264}{11} a^{5} + \frac{9873313128608}{11} a^{4} + \frac{12862550923680}{11} a^{3} - \frac{17940535772736}{11} a^{2} - \frac{14031034128096}{11} a - \frac{2190594640528}{11} \) |
\( \bigl[5 a^{5} - 7 a^{4} - 37 a^{3} + 10 a^{2} + 54 a + 14\) , \( -3 a^{5} + 5 a^{4} + 20 a^{3} - 8 a^{2} - 30 a - 8\) , \( a^{5} - a^{4} - 8 a^{3} + 12 a + 4\) , \( -11 a^{5} + 18 a^{4} + 73 a^{3} - 25 a^{2} - 107 a - 25\) , \( -7 a^{5} + 17 a^{4} + 46 a^{3} - 32 a^{2} - 75 a - 16\bigr] \) |
${y}^2+\left(5a^{5}-7a^{4}-37a^{3}+10a^{2}+54a+14\right){x}{y}+\left(a^{5}-a^{4}-8a^{3}+12a+4\right){y}={x}^{3}+\left(-3a^{5}+5a^{4}+20a^{3}-8a^{2}-30a-8\right){x}^{2}+\left(-11a^{5}+18a^{4}+73a^{3}-25a^{2}-107a-25\right){x}-7a^{5}+17a^{4}+46a^{3}-32a^{2}-75a-16$ |
| 11.2-c2 |
11.2-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.019605582$ |
$36004.48409$ |
3.05500 |
\( \frac{36904356928}{14641} a^{5} + \frac{82788026592}{14641} a^{4} - \frac{36017139104}{14641} a^{3} - \frac{171038556000}{14641} a^{2} - \frac{95350422848}{14641} a - \frac{13760353488}{14641} \) |
\( \bigl[-a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 1\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 8 a - 2\) , \( 5 a^{5} - 7 a^{4} - 37 a^{3} + 10 a^{2} + 54 a + 13\) , \( -2 a^{5} + 4 a^{4} + 12 a^{3} - 10 a^{2} - 14 a - 3\) , \( 3 a^{5} + 3 a^{4} - 42 a^{3} - 22 a^{2} + 86 a + 21\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-9a-1\right){x}{y}+\left(5a^{5}-7a^{4}-37a^{3}+10a^{2}+54a+13\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+3a^{2}-8a-2\right){x}^{2}+\left(-2a^{5}+4a^{4}+12a^{3}-10a^{2}-14a-3\right){x}+3a^{5}+3a^{4}-42a^{3}-22a^{2}+86a+21$ |
| 11.2-c3 |
11.2-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.039211164$ |
$144017.9363$ |
3.05500 |
\( -\frac{21573632}{121} a^{5} + \frac{57974784}{121} a^{4} + \frac{74575872}{121} a^{3} - \frac{104587264}{121} a^{2} - \frac{79351808}{121} a - \frac{11563008}{121} \) |
\( \bigl[0\) , \( -2 a^{5} + 2 a^{4} + 17 a^{3} - 29 a - 8\) , \( 3 a^{5} - 3 a^{4} - 25 a^{3} + a^{2} + 39 a + 12\) , \( 2 a^{5} - 6 a^{4} - 6 a^{3} + 14 a^{2} + 2 a\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 4\bigr] \) |
${y}^2+\left(3a^{5}-3a^{4}-25a^{3}+a^{2}+39a+12\right){y}={x}^{3}+\left(-2a^{5}+2a^{4}+17a^{3}-29a-8\right){x}^{2}+\left(2a^{5}-6a^{4}-6a^{3}+14a^{2}+2a\right){x}-a^{4}+2a^{3}+5a^{2}-6a-4$ |
| 11.2-c4 |
11.2-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.2 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(3a^5-5a^4-20a^3+8a^2+29a+8)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.078422328$ |
$36004.48409$ |
3.05500 |
\( -\frac{154092352}{11} a^{5} - \frac{427127872}{11} a^{4} + \frac{1165148736}{11} a^{3} + \frac{4293921120}{11} a^{2} + \frac{3636110496}{11} a + \frac{855667568}{11} \) |
\( \bigl[a^{5} - a^{4} - 8 a^{3} + 12 a + 5\) , \( 2 a^{4} - 5 a^{3} - 8 a^{2} + 12 a + 5\) , \( 3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 7\) , \( -7 a^{5} + 17 a^{4} + 39 a^{3} - 42 a^{2} - 49 a - 8\) , \( 43 a^{5} - 95 a^{4} - 212 a^{3} + 222 a^{2} + 197 a + 32\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-8a^{3}+12a+5\right){x}{y}+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+7\right){y}={x}^{3}+\left(2a^{4}-5a^{3}-8a^{2}+12a+5\right){x}^{2}+\left(-7a^{5}+17a^{4}+39a^{3}-42a^{2}-49a-8\right){x}+43a^{5}-95a^{4}-212a^{3}+222a^{2}+197a+32$ |
| 11.3-a1 |
11.3-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( -\frac{1480641720039360}{121} a^{5} + \frac{189138657163680}{11} a^{4} + \frac{11002206771662208}{121} a^{3} - \frac{2976913417325472}{121} a^{2} - \frac{16561601010302400}{121} a - \frac{3654542806613744}{121} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 8\) , \( a^{4} - 3 a^{3} - 4 a^{2} + 8 a + 4\) , \( a^{2} - a - 2\) , \( -9 a^{5} + 28 a^{4} + 25 a^{3} - 77 a^{2} + 9 a + 9\) , \( 147 a^{5} - 335 a^{4} - 744 a^{3} + 792 a^{2} + 739 a + 120\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+8\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{4}-3a^{3}-4a^{2}+8a+4\right){x}^{2}+\left(-9a^{5}+28a^{4}+25a^{3}-77a^{2}+9a+9\right){x}+147a^{5}-335a^{4}-744a^{3}+792a^{2}+739a+120$ |
| 11.3-a2 |
11.3-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$32196.47394$ |
2.90297 |
\( -\frac{40951660544}{14641} a^{5} + \frac{4887977984}{1331} a^{4} + \frac{314590838784}{14641} a^{3} - \frac{67768983552}{14641} a^{2} - \frac{484817043456}{14641} a - \frac{108135219200}{14641} \) |
\( \bigl[0\) , \( -2 a^{5} + 3 a^{4} + 14 a^{3} - 3 a^{2} - 22 a - 8\) , \( 1\) , \( 20 a^{5} - 25 a^{4} - 157 a^{3} + 28 a^{2} + 245 a + 58\) , \( 42 a^{5} - 62 a^{4} - 304 a^{3} + 96 a^{2} + 449 a + 97\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-2a^{5}+3a^{4}+14a^{3}-3a^{2}-22a-8\right){x}^{2}+\left(20a^{5}-25a^{4}-157a^{3}+28a^{2}+245a+58\right){x}+42a^{5}-62a^{4}-304a^{3}+96a^{2}+449a+97$ |
| 11.3-a3 |
11.3-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( 11^{8} \) |
$151.28573$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( -\frac{114904730717408}{214358881} a^{5} - \frac{5723565836448}{19487171} a^{4} + \frac{835115215769952}{214358881} a^{3} + \frac{1420657583435168}{214358881} a^{2} + \frac{706961347601824}{214358881} a + \frac{108922183014672}{214358881} \) |
\( \bigl[3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 6\) , \( -5 a^{5} + 7 a^{4} + 37 a^{3} - 10 a^{2} - 55 a - 14\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 6\) , \( -31 a^{5} + 68 a^{4} + 166 a^{3} - 159 a^{2} - 185 a - 33\) , \( 15 a^{5} - 39 a^{4} - 66 a^{3} + 101 a^{2} + 62 a + 9\bigr] \) |
${y}^2+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+6\right){x}{y}+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+6\right){y}={x}^{3}+\left(-5a^{5}+7a^{4}+37a^{3}-10a^{2}-55a-14\right){x}^{2}+\left(-31a^{5}+68a^{4}+166a^{3}-159a^{2}-185a-33\right){x}+15a^{5}-39a^{4}-66a^{3}+101a^{2}+62a+9$ |
| 11.3-a4 |
11.3-a |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(-a^2+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8049.118486$ |
2.90297 |
\( \frac{43690367138208}{121} a^{5} - \frac{9195225620992}{11} a^{4} - \frac{216489213706208}{121} a^{3} + \frac{241026922043136}{121} a^{2} + \frac{207277160730912}{121} a + \frac{33219427739312}{121} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 8\) , \( -a^{5} + a^{4} + 8 a^{3} + a^{2} - 12 a - 7\) , \( 4 a^{5} - 5 a^{4} - 31 a^{3} + 5 a^{2} + 48 a + 13\) , \( 54 a^{5} - 63 a^{4} - 428 a^{3} + 36 a^{2} + 660 a + 232\) , \( -192 a^{5} + 247 a^{4} + 1452 a^{3} - 186 a^{2} - 2214 a - 782\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+8\right){x}{y}+\left(4a^{5}-5a^{4}-31a^{3}+5a^{2}+48a+13\right){y}={x}^{3}+\left(-a^{5}+a^{4}+8a^{3}+a^{2}-12a-7\right){x}^{2}+\left(54a^{5}-63a^{4}-428a^{3}+36a^{2}+660a+232\right){x}-192a^{5}+247a^{4}+1452a^{3}-186a^{2}-2214a-782$ |
| 11.3-b1 |
11.3-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.085148820$ |
$34026.71633$ |
3.13483 |
\( -\frac{171738112}{11} a^{5} + 23001408 a^{4} + \frac{1205850592}{11} a^{3} - \frac{221031968}{11} a^{2} - \frac{1974623584}{11} a - \frac{444855536}{11} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 8\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 4 a - 5\) , \( 3 a^{5} - 4 a^{4} - 23 a^{3} + 6 a^{2} + 35 a + 7\) , \( 7 a^{5} + a^{4} - 81 a^{3} - 29 a^{2} + 155 a + 40\) , \( -72 a^{5} + 139 a^{4} + 432 a^{3} - 291 a^{2} - 537 a - 106\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+8\right){x}{y}+\left(3a^{5}-4a^{4}-23a^{3}+6a^{2}+35a+7\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-4a-5\right){x}^{2}+\left(7a^{5}+a^{4}-81a^{3}-29a^{2}+155a+40\right){x}-72a^{5}+139a^{4}+432a^{3}-291a^{2}-537a-106$ |
| 11.3-b2 |
11.3-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.021287205$ |
$34026.71633$ |
3.13483 |
\( -\frac{886297504}{14641} a^{5} + \frac{34676384}{1331} a^{4} + \frac{8741394848}{14641} a^{3} + \frac{11370488704}{14641} a^{2} + \frac{3463326976}{14641} a + \frac{274010224}{14641} \) |
\( \bigl[3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 6\) , \( a^{5} - a^{4} - 9 a^{3} + 2 a^{2} + 14 a + 1\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 7\) , \( 5 a^{5} - 6 a^{4} - 40 a^{3} + 7 a^{2} + 61 a + 14\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 7\bigr] \) |
${y}^2+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+6\right){x}{y}+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+7\right){y}={x}^{3}+\left(a^{5}-a^{4}-9a^{3}+2a^{2}+14a+1\right){x}^{2}+\left(5a^{5}-6a^{4}-40a^{3}+7a^{2}+61a+14\right){x}+2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+7$ |
| 11.3-b3 |
11.3-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(-a^2+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.042574410$ |
$136106.8653$ |
3.13483 |
\( \frac{359993344}{121} a^{5} - \frac{40566784}{11} a^{4} - \frac{2773073920}{121} a^{3} + \frac{304480256}{121} a^{2} + \frac{4246876160}{121} a + \frac{1502846976}{121} \) |
\( \bigl[0\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 7 a\) , \( a^{5} - a^{4} - 8 a^{3} + 12 a + 4\) , \( -2 a^{5} + a^{4} + 19 a^{3} + 4 a^{2} - 33 a - 11\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 4 a^{2} + 7 a + 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-8a^{3}+12a+4\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+3a^{2}-7a\right){x}^{2}+\left(-2a^{5}+a^{4}+19a^{3}+4a^{2}-33a-11\right){x}+a^{5}-2a^{4}-6a^{3}+4a^{2}+7a+2$ |
| 11.3-b4 |
11.3-b |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.085148820$ |
$34026.71633$ |
3.13483 |
\( \frac{145913137537504}{11} a^{5} - 16443671060512 a^{4} - \frac{1123958157283776}{11} a^{3} + \frac{123436969959328}{11} a^{2} + \frac{1721376690814560}{11} a + \frac{608873940211728}{11} \) |
\( \bigl[5 a^{5} - 7 a^{4} - 37 a^{3} + 10 a^{2} + 54 a + 14\) , \( -2 a^{5} + 3 a^{4} + 14 a^{3} - 4 a^{2} - 19 a - 6\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 5 a^{2} + 8 a + 1\) , \( -17 a^{5} + 22 a^{4} + 129 a^{3} - 20 a^{2} - 196 a - 62\) , \( 14 a^{5} - 13 a^{4} - 118 a^{3} - 10 a^{2} + 190 a + 80\bigr] \) |
${y}^2+\left(5a^{5}-7a^{4}-37a^{3}+10a^{2}+54a+14\right){x}{y}+\left(a^{5}-2a^{4}-6a^{3}+5a^{2}+8a+1\right){y}={x}^{3}+\left(-2a^{5}+3a^{4}+14a^{3}-4a^{2}-19a-6\right){x}^{2}+\left(-17a^{5}+22a^{4}+129a^{3}-20a^{2}-196a-62\right){x}+14a^{5}-13a^{4}-118a^{3}-10a^{2}+190a+80$ |
| 11.3-c1 |
11.3-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.078422328$ |
$36004.48409$ |
3.05500 |
\( -\frac{29411846898624}{11} a^{5} + 3757098582144 a^{4} + \frac{218550661667648}{11} a^{3} - \frac{59134159825120}{11} a^{2} - \frac{328983893673312}{11} a - \frac{72594783410960}{11} \) |
\( \bigl[4 a^{5} - 5 a^{4} - 31 a^{3} + 6 a^{2} + 45 a + 11\) , \( -a^{5} + a^{4} + 9 a^{3} - a^{2} - 17 a - 2\) , \( 1\) , \( -23 a^{5} + 34 a^{4} + 160 a^{3} - 48 a^{2} - 242 a - 52\) , \( -25 a^{5} + 33 a^{4} + 159 a^{3} - 45 a^{2} - 229 a - 50\bigr] \) |
${y}^2+\left(4a^{5}-5a^{4}-31a^{3}+6a^{2}+45a+11\right){x}{y}+{y}={x}^{3}+\left(-a^{5}+a^{4}+9a^{3}-a^{2}-17a-2\right){x}^{2}+\left(-23a^{5}+34a^{4}+160a^{3}-48a^{2}-242a-52\right){x}-25a^{5}+33a^{4}+159a^{3}-45a^{2}-229a-50$ |
| 11.3-c2 |
11.3-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( -11 \) |
$151.28573$ |
$(-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.078422328$ |
$36004.48409$ |
3.05500 |
\( -\frac{1445227264}{11} a^{5} + 368108896 a^{4} + \frac{4546323296}{11} a^{3} - \frac{7525904864}{11} a^{2} - \frac{4555648000}{11} a - \frac{432872432}{11} \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 8\) , \( -2 a^{4} + 5 a^{3} + 8 a^{2} - 11 a - 4\) , \( 3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 7\) , \( -6 a^{5} + 3 a^{4} + 39 a^{3} + 34 a^{2} + 11 a\) , \( -39 a^{5} + 51 a^{4} + 226 a^{3} + 29 a^{2} - 41 a - 9\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+8\right){x}{y}+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+7\right){y}={x}^{3}+\left(-2a^{4}+5a^{3}+8a^{2}-11a-4\right){x}^{2}+\left(-6a^{5}+3a^{4}+39a^{3}+34a^{2}+11a\right){x}-39a^{5}+51a^{4}+226a^{3}+29a^{2}-41a-9$ |
| 11.3-c3 |
11.3-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( 11^{2} \) |
$151.28573$ |
$(-a^2+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.039211164$ |
$144017.9363$ |
3.05500 |
\( -\frac{173527040}{121} a^{5} + \frac{22147072}{11} a^{4} + \frac{1289859072}{121} a^{3} - \frac{347279360}{121} a^{2} - \frac{1943359488}{121} a - \frac{428376064}{121} \) |
\( \bigl[0\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 3 a^{2} + 21 a + 7\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 5 a^{2} + 18 a + 4\) , \( 8 a^{5} - 8 a^{4} - 68 a^{3} + 4 a^{2} + 110 a + 27\) , \( -10 a^{5} + 11 a^{4} + 83 a^{3} - 10 a^{2} - 134 a - 30\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-14a^{3}+5a^{2}+18a+4\right){y}={x}^{3}+\left(2a^{5}-3a^{4}-14a^{3}+3a^{2}+21a+7\right){x}^{2}+\left(8a^{5}-8a^{4}-68a^{3}+4a^{2}+110a+27\right){x}-10a^{5}+11a^{4}+83a^{3}-10a^{2}-134a-30$ |
| 11.3-c4 |
11.3-c |
$4$ |
$4$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
11.3 |
\( 11 \) |
\( 11^{4} \) |
$151.28573$ |
$(-a^2+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.019605582$ |
$36004.48409$ |
3.05500 |
\( \frac{3815085445184}{14641} a^{5} - \frac{802953259936}{1331} a^{4} - \frac{18904657664480}{14641} a^{3} + \frac{21047039349824}{14641} a^{2} + \frac{18101354739232}{14641} a + \frac{2901344871632}{14641} \) |
\( \bigl[4 a^{5} - 5 a^{4} - 31 a^{3} + 5 a^{2} + 48 a + 14\) , \( -3 a^{5} + 5 a^{4} + 20 a^{3} - 8 a^{2} - 29 a - 9\) , \( 4 a^{5} - 5 a^{4} - 31 a^{3} + 5 a^{2} + 48 a + 13\) , \( 3 a^{5} - 6 a^{4} - 14 a^{3} + 8 a^{2} + 9 a - 2\) , \( 2 a^{5} - a^{4} - 15 a^{3} - 5 a^{2} + 13 a + 2\bigr] \) |
${y}^2+\left(4a^{5}-5a^{4}-31a^{3}+5a^{2}+48a+14\right){x}{y}+\left(4a^{5}-5a^{4}-31a^{3}+5a^{2}+48a+13\right){y}={x}^{3}+\left(-3a^{5}+5a^{4}+20a^{3}-8a^{2}-29a-9\right){x}^{2}+\left(3a^{5}-6a^{4}-14a^{3}+8a^{2}+9a-2\right){x}+2a^{5}-a^{4}-15a^{3}-5a^{2}+13a+2$ |
| 16.1-a1 |
16.1-a |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1612.415778$ |
1.16306 |
\( -3018149937104 a^{5} + 4240956964828 a^{4} + 22426969898600 a^{3} - 6068160880724 a^{2} - 33759274753456 a - 7449444293660 \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 8\) , \( 3 a^{5} - 3 a^{4} - 25 a^{3} + 39 a + 12\) , \( 4 a^{5} - 5 a^{4} - 31 a^{3} + 6 a^{2} + 45 a + 11\) , \( -9 a^{5} + 100 a^{3} + 29 a^{2} - 165 a - 71\) , \( -43 a^{5} + 16 a^{4} + 440 a^{3} + 69 a^{2} - 715 a - 278\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+8\right){x}{y}+\left(4a^{5}-5a^{4}-31a^{3}+6a^{2}+45a+11\right){y}={x}^{3}+\left(3a^{5}-3a^{4}-25a^{3}+39a+12\right){x}^{2}+\left(-9a^{5}+100a^{3}+29a^{2}-165a-71\right){x}-43a^{5}+16a^{4}+440a^{3}+69a^{2}-715a-278$ |
| 16.1-a2 |
16.1-a |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$25798.65245$ |
1.16306 |
\( -1523584 a^{5} + 2140864 a^{4} + 11318720 a^{3} - 3061984 a^{2} - 17024544 a - 3743968 \) |
\( \bigl[3 a^{5} - 3 a^{4} - 25 a^{3} + a^{2} + 39 a + 11\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 8 a^{2} - a\) , \( 3 a^{5} - 3 a^{4} - 25 a^{3} + a^{2} + 39 a + 11\) , \( 135 a^{5} - 198 a^{4} - 983 a^{3} + 313 a^{2} + 1459 a + 291\) , \( 1024 a^{5} - 1438 a^{4} - 7606 a^{3} + 2044 a^{2} + 11444 a + 2559\bigr] \) |
${y}^2+\left(3a^{5}-3a^{4}-25a^{3}+a^{2}+39a+11\right){x}{y}+\left(3a^{5}-3a^{4}-25a^{3}+a^{2}+39a+11\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+8a^{2}-a\right){x}^{2}+\left(135a^{5}-198a^{4}-983a^{3}+313a^{2}+1459a+291\right){x}+1024a^{5}-1438a^{4}-7606a^{3}+2044a^{2}+11444a+2559$ |
| 16.1-a3 |
16.1-a |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$25798.65245$ |
1.16306 |
\( 97280 a^{5} - 224704 a^{4} - 483712 a^{3} + 535232 a^{2} + 466560 a + 75328 \) |
\( \bigl[2 a^{5} - 3 a^{4} - 14 a^{3} + 5 a^{2} + 18 a + 5\) , \( 3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 26 a + 7\) , \( 5 a^{5} - 7 a^{4} - 37 a^{3} + 10 a^{2} + 54 a + 14\) , \( 11 a^{5} - 23 a^{4} - 61 a^{3} + 53 a^{2} + 62 a + 12\) , \( 20 a^{5} - 42 a^{4} - 112 a^{3} + 98 a^{2} + 124 a + 24\bigr] \) |
${y}^2+\left(2a^{5}-3a^{4}-14a^{3}+5a^{2}+18a+5\right){x}{y}+\left(5a^{5}-7a^{4}-37a^{3}+10a^{2}+54a+14\right){y}={x}^{3}+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+26a+7\right){x}^{2}+\left(11a^{5}-23a^{4}-61a^{3}+53a^{2}+62a+12\right){x}+20a^{5}-42a^{4}-112a^{3}+98a^{2}+124a+24$ |
| 16.1-a4 |
16.1-a |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$25798.65245$ |
1.16306 |
\( 65354704 a^{5} - 127105564 a^{4} - 513827048 a^{3} + 394762132 a^{2} + 1229893936 a + 403462316 \) |
\( \bigl[4 a^{5} - 5 a^{4} - 31 a^{3} + 6 a^{2} + 45 a + 11\) , \( -3 a^{5} + 5 a^{4} + 20 a^{3} - 8 a^{2} - 28 a - 7\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 8\) , \( -40 a^{5} + 76 a^{4} + 238 a^{3} - 136 a^{2} - 301 a - 101\) , \( 48 a^{5} + 17 a^{4} - 573 a^{3} - 258 a^{2} + 1069 a + 366\bigr] \) |
${y}^2+\left(4a^{5}-5a^{4}-31a^{3}+6a^{2}+45a+11\right){x}{y}+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+8\right){y}={x}^{3}+\left(-3a^{5}+5a^{4}+20a^{3}-8a^{2}-28a-7\right){x}^{2}+\left(-40a^{5}+76a^{4}+238a^{3}-136a^{2}-301a-101\right){x}+48a^{5}+17a^{4}-573a^{3}-258a^{2}+1069a+366$ |
| 16.1-a5 |
16.1-a |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1612.415778$ |
1.16306 |
\( -34764180446060324 a^{5} - 16277133707680014 a^{4} + 254215107677712140 a^{3} + 408006807153320956 a^{2} + 181871847002346226 a + 23677842389385800 \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + a^{2} + 27 a + 8\) , \( 3 a^{5} - 3 a^{4} - 25 a^{3} + 39 a + 12\) , \( -a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 1\) , \( -106 a^{5} + 132 a^{4} + 814 a^{3} - 92 a^{2} - 1249 a - 441\) , \( 414 a^{5} - 485 a^{4} - 3267 a^{3} + 271 a^{2} + 5031 a + 1795\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+a^{2}+27a+8\right){x}{y}+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-9a-1\right){y}={x}^{3}+\left(3a^{5}-3a^{4}-25a^{3}+39a+12\right){x}^{2}+\left(-106a^{5}+132a^{4}+814a^{3}-92a^{2}-1249a-441\right){x}+414a^{5}-485a^{4}-3267a^{3}+271a^{2}+5031a+1795$ |
| 16.1-a6 |
16.1-a |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1612.415778$ |
1.16306 |
\( 12734192037200676 a^{5} - 15785876748254962 a^{4} - 98090521314072332 a^{3} + 10772681110396420 a^{2} + 150228644572197646 a + 53137871684944264 \) |
\( \bigl[3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 6\) , \( -2 a^{5} + 4 a^{4} + 12 a^{3} - 9 a^{2} - 16 a - 3\) , \( a^{5} - 11 a^{3} - 3 a^{2} + 18 a + 5\) , \( -1058 a^{5} + 2449 a^{4} + 5249 a^{3} - 5842 a^{2} - 5052 a - 814\) , \( -28268 a^{5} + 65451 a^{4} + 140068 a^{3} - 155988 a^{2} - 134135 a - 21496\bigr] \) |
${y}^2+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+6\right){x}{y}+\left(a^{5}-11a^{3}-3a^{2}+18a+5\right){y}={x}^{3}+\left(-2a^{5}+4a^{4}+12a^{3}-9a^{2}-16a-3\right){x}^{2}+\left(-1058a^{5}+2449a^{4}+5249a^{3}-5842a^{2}-5052a-814\right){x}-28268a^{5}+65451a^{4}+140068a^{3}-155988a^{2}-134135a-21496$ |
| 16.1-b1 |
16.1-b |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1612.415778$ |
1.16306 |
\( -161544038721929406 a^{5} + 433115614011031674 a^{4} + 564241972585547060 a^{3} - 787002888979382118 a^{2} - 615498379775395750 a - 96094276890558620 \) |
\( \bigl[-a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 1\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 25 a + 4\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 5\) , \( -353 a^{5} + 493 a^{4} + 2622 a^{3} - 671 a^{2} - 3945 a - 939\) , \( -32202 a^{5} + 45097 a^{4} + 239534 a^{3} - 63679 a^{2} - 360763 a - 81031\bigr] \) |
${y}^2+\left(-a^{5}+2a^{4}+6a^{3}-4a^{2}-9a-1\right){x}{y}+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+5\right){y}={x}^{3}+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+25a+4\right){x}^{2}+\left(-353a^{5}+493a^{4}+2622a^{3}-671a^{2}-3945a-939\right){x}-32202a^{5}+45097a^{4}+239534a^{3}-63679a^{2}-360763a-81031$ |
| 16.1-b2 |
16.1-b |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{16} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$1612.415778$ |
1.16306 |
\( 42023326207166 a^{5} + 91227615944070 a^{4} - 46632489839412 a^{3} - 189342552900250 a^{2} - 96543815274586 a - 13134632940948 \) |
\( \bigl[2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 5\) , \( 6 a^{5} - 9 a^{4} - 43 a^{3} + 14 a^{2} + 63 a + 14\) , \( 3 a^{5} - 5 a^{4} - 20 a^{3} + 9 a^{2} + 27 a + 6\) , \( -498 a^{5} + 1146 a^{4} + 2466 a^{3} - 2693 a^{2} - 2299 a - 370\) , \( 19605 a^{5} - 45366 a^{4} - 97152 a^{3} + 108001 a^{2} + 92853 a + 14874\bigr] \) |
${y}^2+\left(2a^{5}-2a^{4}-17a^{3}+2a^{2}+26a+5\right){x}{y}+\left(3a^{5}-5a^{4}-20a^{3}+9a^{2}+27a+6\right){y}={x}^{3}+\left(6a^{5}-9a^{4}-43a^{3}+14a^{2}+63a+14\right){x}^{2}+\left(-498a^{5}+1146a^{4}+2466a^{3}-2693a^{2}-2299a-370\right){x}+19605a^{5}-45366a^{4}-97152a^{3}+108001a^{2}+92853a+14874$ |
| 16.1-b3 |
16.1-b |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$25798.65245$ |
1.16306 |
\( -124665900 a^{5} + 335962120 a^{4} + 435364164 a^{3} - 610508496 a^{2} - 475758612 a - 73973000 \) |
\( \bigl[4 a^{5} - 5 a^{4} - 31 a^{3} + 6 a^{2} + 45 a + 11\) , \( 5 a^{5} - 7 a^{4} - 37 a^{3} + 10 a^{2} + 53 a + 14\) , \( 0\) , \( 32 a^{5} + 45 a^{4} - 271 a^{3} - 542 a^{2} - 248 a - 30\) , \( 376 a^{5} + 207 a^{4} - 2786 a^{3} - 4562 a^{2} - 2044 a - 266\bigr] \) |
${y}^2+\left(4a^{5}-5a^{4}-31a^{3}+6a^{2}+45a+11\right){x}{y}={x}^{3}+\left(5a^{5}-7a^{4}-37a^{3}+10a^{2}+53a+14\right){x}^{2}+\left(32a^{5}+45a^{4}-271a^{3}-542a^{2}-248a-30\right){x}+376a^{5}+207a^{4}-2786a^{3}-4562a^{2}-2044a-266$ |
| 16.1-b4 |
16.1-b |
$6$ |
$8$ |
6.6.1922000.1 |
$6$ |
$[6, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$156.08407$ |
$(3a^5-4a^4-23a^3+5a^2+36a+11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 1 \) |
$1$ |
$25798.65245$ |
1.16306 |
\( -45632 a^{5} - 8736 a^{4} + 321120 a^{3} + 465248 a^{2} + 190720 a + 25152 \) |
\( \bigl[3 a^{5} - 3 a^{4} - 25 a^{3} + a^{2} + 39 a + 11\) , \( 4 a^{5} - 6 a^{4} - 29 a^{3} + 10 a^{2} + 44 a + 10\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 5 a^{2} + 18 a + 5\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 6 a^{2} - 1\) , \( a^{5} + 3 a^{4} - 8 a^{3} - 26 a^{2} - 13 a - 2\bigr] \) |
${y}^2+\left(3a^{5}-3a^{4}-25a^{3}+a^{2}+39a+11\right){x}{y}+\left(2a^{5}-3a^{4}-14a^{3}+5a^{2}+18a+5\right){y}={x}^{3}+\left(4a^{5}-6a^{4}-29a^{3}+10a^{2}+44a+10\right){x}^{2}+\left(2a^{5}-4a^{4}-8a^{3}+6a^{2}-1\right){x}+a^{5}+3a^{4}-8a^{3}-26a^{2}-13a-2$ |
*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.
