| 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 |
| 19.1-a1 |
19.1-a |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(4a^3+7a^2-36a-45)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.019605404$ |
$1650.734053$ |
3.157813394 |
\( \frac{1206945434}{6859} a^{3} - \frac{3612989771}{6859} a^{2} - \frac{1259178311}{6859} a + \frac{5062239805}{6859} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 4 a^{3} + 7 a^{2} - 35 a - 42\) , \( 0\) , \( 13 a^{3} + 8 a^{2} - 125 a + 12\) , \( 20 a^{3} - 21 a^{2} - 216 a + 336\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+27a+30\right){x}{y}={x}^{3}+\left(4a^{3}+7a^{2}-35a-42\right){x}^{2}+\left(13a^{3}+8a^{2}-125a+12\right){x}+20a^{3}-21a^{2}-216a+336$ |
| 19.1-b1 |
19.1-b |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(4a^3+7a^2-36a-45)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$242.4834118$ |
1.971670517 |
\( \frac{1206945434}{6859} a^{3} - \frac{3612989771}{6859} a^{2} - \frac{1259178311}{6859} a + \frac{5062239805}{6859} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 27 a + 31\) , \( 2 a^{3} + 3 a^{2} - 18 a - 16\) , \( a + 1\) , \( 6 a^{3} + 8 a^{2} - 54 a - 41\) , \( a^{3} - 3 a^{2} - 10 a + 28\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+27a+31\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-18a-16\right){x}^{2}+\left(6a^{3}+8a^{2}-54a-41\right){x}+a^{3}-3a^{2}-10a+28$ |
| 19.1-c1 |
19.1-c |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(4a^3+7a^2-36a-45)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$58.43384051$ |
0.475134689 |
\( \frac{1206945434}{6859} a^{3} - \frac{3612989771}{6859} a^{2} - \frac{1259178311}{6859} a + \frac{5062239805}{6859} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 13\) , \( 3 a^{3} + 5 a^{2} - 26 a - 31\) , \( -3 a^{3} - 5 a^{2} + 28 a + 30\) , \( -6 a^{3} - 10 a^{2} + 52 a + 61\) , \( -16 a^{3} - 30 a^{2} + 139 a + 170\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-13\right){x}{y}+\left(-3a^{3}-5a^{2}+28a+30\right){y}={x}^{3}+\left(3a^{3}+5a^{2}-26a-31\right){x}^{2}+\left(-6a^{3}-10a^{2}+52a+61\right){x}-16a^{3}-30a^{2}+139a+170$ |
| 19.1-d1 |
19.1-d |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(4a^3+7a^2-36a-45)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.097238852$ |
$397.7951713$ |
3.774269320 |
\( \frac{1206945434}{6859} a^{3} - \frac{3612989771}{6859} a^{2} - \frac{1259178311}{6859} a + \frac{5062239805}{6859} \) |
\( \bigl[a + 1\) , \( 4 a^{3} + 7 a^{2} - 36 a - 42\) , \( a^{3} + 2 a^{2} - 8 a - 13\) , \( -44 a^{3} - 84 a^{2} + 383 a + 504\) , \( 37 a^{3} + 69 a^{2} - 323 a - 411\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+2a^{2}-8a-13\right){y}={x}^{3}+\left(4a^{3}+7a^{2}-36a-42\right){x}^{2}+\left(-44a^{3}-84a^{2}+383a+504\right){x}+37a^{3}+69a^{2}-323a-411$ |
| 19.2-a1 |
19.2-a |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(-a^3-a^2+9a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.019605404$ |
$1650.734053$ |
3.157813394 |
\( -\frac{38530788356}{6859} a^{3} - \frac{71034696073}{6859} a^{2} + \frac{17745987611}{361} a + \frac{419195808212}{6859} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 18\) , \( -2 a^{3} - 3 a^{2} + 17 a + 16\) , \( -2 a^{3} - 3 a^{2} + 18 a + 18\) , \( -62 a^{3} - 108 a^{2} + 569 a + 692\) , \( -182 a^{3} - 320 a^{2} + 1665 a + 2042\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+18\right){x}{y}+\left(-2a^{3}-3a^{2}+18a+18\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+17a+16\right){x}^{2}+\left(-62a^{3}-108a^{2}+569a+692\right){x}-182a^{3}-320a^{2}+1665a+2042$ |
| 19.2-b1 |
19.2-b |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(-a^3-a^2+9a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$242.4834118$ |
1.971670517 |
\( -\frac{38530788356}{6859} a^{3} - \frac{71034696073}{6859} a^{2} + \frac{17745987611}{361} a + \frac{419195808212}{6859} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 17\) , \( -3 a^{3} - 5 a^{2} + 27 a + 29\) , \( -3 a^{3} - 5 a^{2} + 28 a + 31\) , \( -6 a^{3} - 10 a^{2} + 54 a + 59\) , \( -4 a^{3} - 7 a^{2} + 36 a + 42\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+17\right){x}{y}+\left(-3a^{3}-5a^{2}+28a+31\right){y}={x}^{3}+\left(-3a^{3}-5a^{2}+27a+29\right){x}^{2}+\left(-6a^{3}-10a^{2}+54a+59\right){x}-4a^{3}-7a^{2}+36a+42$ |
| 19.2-c1 |
19.2-c |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(-a^3-a^2+9a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$58.43384051$ |
0.475134689 |
\( -\frac{38530788356}{6859} a^{3} - \frac{71034696073}{6859} a^{2} + \frac{17745987611}{361} a + \frac{419195808212}{6859} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 13\) , \( -3 a^{3} - 5 a^{2} + 26 a + 30\) , \( -3 a^{3} - 5 a^{2} + 28 a + 31\) , \( a^{3} + 2 a^{2} - 6 a - 13\) , \( 4 a^{3} + 4 a^{2} - 32 a - 39\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-13\right){x}{y}+\left(-3a^{3}-5a^{2}+28a+31\right){y}={x}^{3}+\left(-3a^{3}-5a^{2}+26a+30\right){x}^{2}+\left(a^{3}+2a^{2}-6a-13\right){x}+4a^{3}+4a^{2}-32a-39$ |
| 19.2-d1 |
19.2-d |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(-a^3-a^2+9a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.097238852$ |
$397.7951713$ |
3.774269320 |
\( -\frac{38530788356}{6859} a^{3} - \frac{71034696073}{6859} a^{2} + \frac{17745987611}{361} a + \frac{419195808212}{6859} \) |
\( \bigl[a^{3} + 2 a^{2} - 8 a - 12\) , \( -2 a^{3} - 3 a^{2} + 17 a + 16\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( -11 a^{3} - 27 a^{2} + 112 a + 150\) , \( 11 a^{3} + 32 a^{2} - 122 a - 166\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-8a-12\right){x}{y}+\left(a^{3}+2a^{2}-9a-12\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+17a+16\right){x}^{2}+\left(-11a^{3}-27a^{2}+112a+150\right){x}+11a^{3}+32a^{2}-122a-166$ |
| 19.3-a1 |
19.3-a |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(6a^3+11a^2-53a-65)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.019605404$ |
$1650.734053$ |
3.157813394 |
\( \frac{39656807629}{6859} a^{3} + \frac{69710284663}{6859} a^{2} - \frac{362938149300}{6859} a - \frac{445724222643}{6859} \) |
\( \bigl[a^{3} + 2 a^{2} - 8 a - 13\) , \( 4 a^{3} + 7 a^{2} - 37 a - 43\) , \( -2 a^{3} - 3 a^{2} + 18 a + 17\) , \( -6 a^{3} + a^{2} + 39 a + 27\) , \( -a^{3} + 41 a^{2} - 62 a - 132\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-8a-13\right){x}{y}+\left(-2a^{3}-3a^{2}+18a+17\right){y}={x}^{3}+\left(4a^{3}+7a^{2}-37a-43\right){x}^{2}+\left(-6a^{3}+a^{2}+39a+27\right){x}-a^{3}+41a^{2}-62a-132$ |
| 19.3-b1 |
19.3-b |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(6a^3+11a^2-53a-65)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$242.4834118$ |
1.971670517 |
\( \frac{39656807629}{6859} a^{3} + \frac{69710284663}{6859} a^{2} - \frac{362938149300}{6859} a - \frac{445724222643}{6859} \) |
\( \bigl[a^{3} + 2 a^{2} - 8 a - 12\) , \( -a - 1\) , \( -2 a^{3} - 3 a^{2} + 19 a + 17\) , \( 5 a^{3} + 10 a^{2} - 47 a - 64\) , \( 4 a^{3} + 9 a^{2} - 38 a - 57\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-8a-12\right){x}{y}+\left(-2a^{3}-3a^{2}+19a+17\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a^{3}+10a^{2}-47a-64\right){x}+4a^{3}+9a^{2}-38a-57$ |
| 19.3-c1 |
19.3-c |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(6a^3+11a^2-53a-65)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$58.43384051$ |
0.475134689 |
\( \frac{39656807629}{6859} a^{3} + \frac{69710284663}{6859} a^{2} - \frac{362938149300}{6859} a - \frac{445724222643}{6859} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 12\) , \( 2 a^{3} + 3 a^{2} - 19 a - 18\) , \( -2 a^{3} - 3 a^{2} + 19 a + 17\) , \( -7 a^{3} - 11 a^{2} + 64 a + 65\) , \( 3 a^{3} + 11 a^{2} - 24 a - 91\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-12\right){x}{y}+\left(-2a^{3}-3a^{2}+19a+17\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-19a-18\right){x}^{2}+\left(-7a^{3}-11a^{2}+64a+65\right){x}+3a^{3}+11a^{2}-24a-91$ |
| 19.3-d1 |
19.3-d |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(6a^3+11a^2-53a-65)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.097238852$ |
$397.7951713$ |
3.774269320 |
\( \frac{39656807629}{6859} a^{3} + \frac{69710284663}{6859} a^{2} - \frac{362938149300}{6859} a - \frac{445724222643}{6859} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 27 a + 31\) , \( 4 a^{3} + 7 a^{2} - 37 a - 43\) , \( a^{3} + 2 a^{2} - 8 a - 13\) , \( -2 a^{3} + 11 a^{2} + 23 a - 105\) , \( 6 a^{3} - 16 a^{2} - 73 a + 196\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+27a+31\right){x}{y}+\left(a^{3}+2a^{2}-8a-13\right){y}={x}^{3}+\left(4a^{3}+7a^{2}-37a-43\right){x}^{2}+\left(-2a^{3}+11a^{2}+23a-105\right){x}+6a^{3}-16a^{2}-73a+196$ |
| 19.4-a1 |
19.4-a |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(-a^3-a^2+9a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.019605404$ |
$1650.734053$ |
3.157813394 |
\( -\frac{2332964707}{6859} a^{3} + \frac{4937401181}{6859} a^{2} + \frac{27023563002}{6859} a - \frac{63113802390}{6859} \) |
\( \bigl[a\) , \( -3 a^{3} - 5 a^{2} + 28 a + 31\) , \( 0\) , \( 57 a^{3} + 106 a^{2} - 495 a - 617\) , \( 235 a^{3} + 434 a^{2} - 2054 a - 2557\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-3a^{3}-5a^{2}+28a+31\right){x}^{2}+\left(57a^{3}+106a^{2}-495a-617\right){x}+235a^{3}+434a^{2}-2054a-2557$ |
| 19.4-b1 |
19.4-b |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(-a^3-a^2+9a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$242.4834118$ |
1.971670517 |
\( -\frac{2332964707}{6859} a^{3} + \frac{4937401181}{6859} a^{2} + \frac{27023563002}{6859} a - \frac{63113802390}{6859} \) |
\( \bigl[a + 1\) , \( a^{3} + 2 a^{2} - 9 a - 14\) , \( -2 a^{3} - 3 a^{2} + 19 a + 18\) , \( 9 a^{3} + 17 a^{2} - 80 a - 108\) , \( 11 a^{3} + 21 a^{2} - 97 a - 131\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-2a^{3}-3a^{2}+19a+18\right){y}={x}^{3}+\left(a^{3}+2a^{2}-9a-14\right){x}^{2}+\left(9a^{3}+17a^{2}-80a-108\right){x}+11a^{3}+21a^{2}-97a-131$ |
| 19.4-c1 |
19.4-c |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(-a^3-a^2+9a+6)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$58.43384051$ |
0.475134689 |
\( -\frac{2332964707}{6859} a^{3} + \frac{4937401181}{6859} a^{2} + \frac{27023563002}{6859} a - \frac{63113802390}{6859} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 12\) , \( -2 a^{3} - 3 a^{2} + 19 a + 17\) , \( -2 a^{3} - 3 a^{2} + 19 a + 18\) , \( 4 a^{3} + 6 a^{2} - 37 a - 36\) , \( 25 a^{3} + 45 a^{2} - 228 a - 292\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-12\right){x}{y}+\left(-2a^{3}-3a^{2}+19a+18\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+19a+17\right){x}^{2}+\left(4a^{3}+6a^{2}-37a-36\right){x}+25a^{3}+45a^{2}-228a-292$ |
| 19.4-d1 |
19.4-d |
$1$ |
$1$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( - 19^{3} \) |
$15.87927$ |
$(-a^3-a^2+9a+6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.097238852$ |
$397.7951713$ |
3.774269320 |
\( -\frac{2332964707}{6859} a^{3} + \frac{4937401181}{6859} a^{2} + \frac{27023563002}{6859} a - \frac{63113802390}{6859} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 17\) , \( -3 a^{3} - 5 a^{2} + 28 a + 31\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 55 a^{3} + 98 a^{2} - 499 a - 620\) , \( -42 a^{3} - 74 a^{2} + 383 a + 469\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+17\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(-3a^{3}-5a^{2}+28a+31\right){x}^{2}+\left(55a^{3}+98a^{2}-499a-620\right){x}-42a^{3}-74a^{2}+383a+469$ |
| 55.1-a1 |
55.1-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$394.7006986$ |
1.426388029 |
\( -\frac{48555143354501}{275} a^{3} - \frac{97110286709002}{275} a^{2} + \frac{436996290190509}{275} a + \frac{661225593030336}{275} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 12\) , \( -a^{3} - 2 a^{2} + 9 a + 13\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( 4 a^{3} + 8 a^{2} - 36 a - 78\) , \( -29 a^{3} - 58 a^{2} + 261 a + 385\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-12\right){x}{y}+\left(a^{3}+2a^{2}-9a-12\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+9a+13\right){x}^{2}+\left(4a^{3}+8a^{2}-36a-78\right){x}-29a^{3}-58a^{2}+261a+385$ |
| 55.1-a2 |
55.1-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$19.49139252$ |
1.426388029 |
\( -\frac{754904381777}{33275} a^{3} - \frac{1509808763554}{33275} a^{2} + \frac{6794139435993}{33275} a + \frac{2056062822711}{6655} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 12\) , \( -a^{3} - 2 a^{2} + 9 a + 13\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( 4 a^{3} + 8 a^{2} - 36 a - 53\) , \( -2 a^{3} - 4 a^{2} + 18 a + 9\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-12\right){x}{y}+\left(a^{3}+2a^{2}-9a-12\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+9a+13\right){x}^{2}+\left(4a^{3}+8a^{2}-36a-53\right){x}-2a^{3}-4a^{2}+18a+9$ |
| 55.1-a3 |
55.1-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1578.802794$ |
1.426388029 |
\( -\frac{45227}{55} a^{3} - \frac{90454}{55} a^{2} + \frac{407043}{55} a + \frac{122986}{11} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 12\) , \( -a^{3} - 2 a^{2} + 9 a + 13\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( -a^{3} - 2 a^{2} + 9 a + 12\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-12\right){x}{y}+\left(a^{3}+2a^{2}-9a-12\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+9a+13\right){x}^{2}+\left(-a^{3}-2a^{2}+9a+12\right){x}$ |
| 55.1-a4 |
55.1-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$1578.802794$ |
1.426388029 |
\( -\frac{132583563}{605} a^{3} - \frac{265167126}{605} a^{2} + \frac{1193252067}{605} a + \frac{1889656801}{605} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 12\) , \( -a^{3} - 2 a^{2} + 9 a + 13\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( -6 a^{3} - 12 a^{2} + 54 a + 67\) , \( 8 a^{3} + 16 a^{2} - 72 a - 91\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-12\right){x}{y}+\left(a^{3}+2a^{2}-9a-12\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+9a+13\right){x}^{2}+\left(-6a^{3}-12a^{2}+54a+67\right){x}+8a^{3}+16a^{2}-72a-91$ |
| 55.1-a5 |
55.1-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{24} \cdot 11^{6} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2^{2} \) |
$1$ |
$4.872848131$ |
1.426388029 |
\( \frac{4560282420936767}{20796875} a^{3} + \frac{9120564841873534}{20796875} a^{2} - \frac{41042541788430903}{20796875} a - \frac{51904810910436359}{20796875} \) |
\( \bigl[1\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( 1\) , \( 16 a^{3} + 32 a^{2} - 144 a - 418\) , \( -1110 a^{3} - 2220 a^{2} + 9990 a + 13896\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{3}+2a^{2}-9a-12\right){x}^{2}+\left(16a^{3}+32a^{2}-144a-418\right){x}-1110a^{3}-2220a^{2}+9990a+13896$ |
| 55.1-a6 |
55.1-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{12} \cdot 11^{12} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$36$ |
\( 2^{2} \) |
$1$ |
$19.49139252$ |
1.426388029 |
\( \frac{1485675267531}{221445125} a^{3} + \frac{2971350535062}{221445125} a^{2} - \frac{13371077407779}{221445125} a - \frac{15161713818194}{221445125} \) |
\( \bigl[1\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( 1\) , \( 21 a^{3} + 42 a^{2} - 189 a - 298\) , \( 54 a^{3} + 108 a^{2} - 486 a - 760\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{3}+2a^{2}-9a-12\right){x}^{2}+\left(21a^{3}+42a^{2}-189a-298\right){x}+54a^{3}+108a^{2}-486a-760$ |
| 55.1-a7 |
55.1-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$394.7006986$ |
1.426388029 |
\( \frac{626283905886387}{73205} a^{3} + \frac{1252567811772774}{73205} a^{2} - \frac{5636555152977483}{73205} a - \frac{1425668429911408}{14641} \) |
\( \bigl[1\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( 1\) , \( -9 a^{3} - 18 a^{2} + 81 a + 92\) , \( 6 a^{3} + 12 a^{2} - 54 a - 34\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{3}+2a^{2}-9a-12\right){x}^{2}+\left(-9a^{3}-18a^{2}+81a+92\right){x}+6a^{3}+12a^{2}-54a-34$ |
| 55.1-a8 |
55.1-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{24} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2^{2} \) |
$1$ |
$4.872848131$ |
1.426388029 |
\( \frac{114278307303626907}{78460709418025} a^{3} + \frac{228556614607253814}{78460709418025} a^{2} - \frac{1028504765732642163}{78460709418025} a - \frac{256402923382212311}{15692141883605} \) |
\( \bigl[1\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( 1\) , \( -54 a^{3} - 108 a^{2} + 486 a + 702\) , \( 374 a^{3} + 748 a^{2} - 3366 a - 5060\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{3}+2a^{2}-9a-12\right){x}^{2}+\left(-54a^{3}-108a^{2}+486a+702\right){x}+374a^{3}+748a^{2}-3366a-5060$ |
| 55.1-b1 |
55.1-b |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$87.42000032$ |
2.843302739 |
\( \frac{626283905886387}{73205} a^{3} + \frac{1252567811772774}{73205} a^{2} - \frac{5636555152977483}{73205} a - \frac{1425668429911408}{14641} \) |
\( \bigl[a^{3} + 2 a^{2} - 8 a - 13\) , \( a^{3} + 2 a^{2} - 8 a - 12\) , \( a + 1\) , \( -10 a^{3} - 37 a^{2} + 3 a + 35\) , \( 6333 a^{3} + 11258 a^{2} - 57383 a - 70693\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-8a-13\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+2a^{2}-8a-12\right){x}^{2}+\left(-10a^{3}-37a^{2}+3a+35\right){x}+6333a^{3}+11258a^{2}-57383a-70693$ |
| 55.1-b2 |
55.1-b |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$155.4133339$ |
2.843302739 |
\( -\frac{754904381777}{33275} a^{3} - \frac{1509808763554}{33275} a^{2} + \frac{6794139435993}{33275} a + \frac{2056062822711}{6655} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 17\) , \( -a^{3} - 2 a^{2} + 9 a + 14\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 164 a^{3} + 299 a^{2} - 1446 a - 1782\) , \( -9203 a^{3} - 16980 a^{2} + 80539 a + 100298\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+17\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+9a+14\right){x}^{2}+\left(164a^{3}+299a^{2}-1446a-1782\right){x}-9203a^{3}-16980a^{2}+80539a+100298$ |
| 55.1-b3 |
55.1-b |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \) |
$1$ |
$21.85500008$ |
2.843302739 |
\( -\frac{48555143354501}{275} a^{3} - \frac{97110286709002}{275} a^{2} + \frac{436996290190509}{275} a + \frac{661225593030336}{275} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 27 a + 31\) , \( -a^{3} - 2 a^{2} + 9 a + 14\) , \( -2 a^{3} - 3 a^{2} + 18 a + 18\) , \( 14 a^{3} - 118 a^{2} + 169 a + 150\) , \( 79 a^{3} - 487 a^{2} + 718 a + 79\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+27a+31\right){x}{y}+\left(-2a^{3}-3a^{2}+18a+18\right){y}={x}^{3}+\left(-a^{3}-2a^{2}+9a+14\right){x}^{2}+\left(14a^{3}-118a^{2}+169a+150\right){x}+79a^{3}-487a^{2}+718a+79$ |
| 55.1-b4 |
55.1-b |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{12} \cdot 11^{12} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$38.85333347$ |
2.843302739 |
\( \frac{1485675267531}{221445125} a^{3} + \frac{2971350535062}{221445125} a^{2} - \frac{13371077407779}{221445125} a - \frac{15161713818194}{221445125} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 28 a + 31\) , \( -1\) , \( a^{3} + 2 a^{2} - 9 a - 13\) , \( -21 a^{3} - 90 a^{2} + 379 a + 133\) , \( 245 a^{3} - 1115 a^{2} - 207 a + 3972\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+28a+31\right){x}{y}+\left(a^{3}+2a^{2}-9a-13\right){y}={x}^{3}-{x}^{2}+\left(-21a^{3}-90a^{2}+379a+133\right){x}+245a^{3}-1115a^{2}-207a+3972$ |
| 55.1-b5 |
55.1-b |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$349.6800013$ |
2.843302739 |
\( -\frac{132583563}{605} a^{3} - \frac{265167126}{605} a^{2} + \frac{1193252067}{605} a + \frac{1889656801}{605} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 28 a + 31\) , \( -1\) , \( a^{3} + 2 a^{2} - 9 a - 13\) , \( -26 a^{3} - 50 a^{2} + 269 a + 238\) , \( -54 a^{3} + 31 a^{2} + 376 a - 77\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+28a+31\right){x}{y}+\left(a^{3}+2a^{2}-9a-13\right){y}={x}^{3}-{x}^{2}+\left(-26a^{3}-50a^{2}+269a+238\right){x}-54a^{3}+31a^{2}+376a-77$ |
| 55.1-b6 |
55.1-b |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1398.720005$ |
2.843302739 |
\( -\frac{45227}{55} a^{3} - \frac{90454}{55} a^{2} + \frac{407043}{55} a + \frac{122986}{11} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 28 a + 31\) , \( -1\) , \( a^{3} + 2 a^{2} - 9 a - 13\) , \( -26 a^{3} - 45 a^{2} + 239 a + 283\) , \( -31 a^{3} - 51 a^{2} + 279 a + 333\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+28a+31\right){x}{y}+\left(a^{3}+2a^{2}-9a-13\right){y}={x}^{3}-{x}^{2}+\left(-26a^{3}-45a^{2}+239a+283\right){x}-31a^{3}-51a^{2}+279a+333$ |
| 55.1-b7 |
55.1-b |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{24} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$9.713333369$ |
2.843302739 |
\( \frac{114278307303626907}{78460709418025} a^{3} + \frac{228556614607253814}{78460709418025} a^{2} - \frac{1028504765732642163}{78460709418025} a - \frac{256402923382212311}{15692141883605} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 28 a + 30\) , \( -2 a^{3} - 3 a^{2} + 17 a + 18\) , \( a^{3} + 2 a^{2} - 8 a - 13\) , \( -1990 a^{3} - 3646 a^{2} + 17525 a + 21774\) , \( 23534 a^{3} + 44053 a^{2} - 203035 a - 253937\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+28a+30\right){x}{y}+\left(a^{3}+2a^{2}-8a-13\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+17a+18\right){x}^{2}+\left(-1990a^{3}-3646a^{2}+17525a+21774\right){x}+23534a^{3}+44053a^{2}-203035a-253937$ |
| 55.1-b8 |
55.1-b |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{24} \cdot 11^{6} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$2.428333342$ |
2.843302739 |
\( \frac{4560282420936767}{20796875} a^{3} + \frac{9120564841873534}{20796875} a^{2} - \frac{41042541788430903}{20796875} a - \frac{51904810910436359}{20796875} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 28 a + 30\) , \( -2 a^{3} - 3 a^{2} + 17 a + 18\) , \( a^{3} + 2 a^{2} - 8 a - 13\) , \( -9340 a^{3} - 17296 a^{2} + 81435 a + 101504\) , \( -548282 a^{3} - 1012793 a^{2} + 4792417 a + 5969483\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+28a+30\right){x}{y}+\left(a^{3}+2a^{2}-8a-13\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+17a+18\right){x}^{2}+\left(-9340a^{3}-17296a^{2}+81435a+101504\right){x}-548282a^{3}-1012793a^{2}+4792417a+5969483$ |
| 55.1-c1 |
55.1-c |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.119930090$ |
$49.42453178$ |
6.940416381 |
\( -\frac{754904381777}{33275} a^{3} - \frac{1509808763554}{33275} a^{2} + \frac{6794139435993}{33275} a + \frac{2056062822711}{6655} \) |
\( \bigl[a + 1\) , \( 3 a^{3} + 5 a^{2} - 28 a - 29\) , \( -2 a^{3} - 3 a^{2} + 18 a + 17\) , \( 60 a^{3} + 125 a^{2} - 517 a - 787\) , \( 2494 a^{3} + 4691 a^{2} - 21760 a - 28020\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(-2a^{3}-3a^{2}+18a+17\right){y}={x}^{3}+\left(3a^{3}+5a^{2}-28a-29\right){x}^{2}+\left(60a^{3}+125a^{2}-517a-787\right){x}+2494a^{3}+4691a^{2}-21760a-28020$ |
| 55.1-c2 |
55.1-c |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.029982522$ |
$444.8207860$ |
6.940416381 |
\( -\frac{48555143354501}{275} a^{3} - \frac{97110286709002}{275} a^{2} + \frac{436996290190509}{275} a + \frac{661225593030336}{275} \) |
\( \bigl[a^{3} + 2 a^{2} - 8 a - 12\) , \( -2 a^{3} - 3 a^{2} + 18 a + 16\) , \( -2 a^{3} - 3 a^{2} + 19 a + 17\) , \( 263 a^{3} + 394 a^{2} - 2291 a - 2733\) , \( -2090 a^{3} - 3526 a^{2} + 18870 a + 22995\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-8a-12\right){x}{y}+\left(-2a^{3}-3a^{2}+19a+17\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+18a+16\right){x}^{2}+\left(263a^{3}+394a^{2}-2291a-2733\right){x}-2090a^{3}-3526a^{2}+18870a+22995$ |
| 55.1-c3 |
55.1-c |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$0.479720362$ |
$27.80129912$ |
6.940416381 |
\( \frac{626283905886387}{73205} a^{3} + \frac{1252567811772774}{73205} a^{2} - \frac{5636555152977483}{73205} a - \frac{1425668429911408}{14641} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 19 a + 18\) , \( 2 a^{3} + 3 a^{2} - 18 a - 16\) , \( -3 a^{3} - 5 a^{2} + 28 a + 31\) , \( 525 a^{3} + 906 a^{2} - 4781 a - 5821\) , \( -16874 a^{3} - 29751 a^{2} + 154508 a + 189916\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+19a+18\right){x}{y}+\left(-3a^{3}-5a^{2}+28a+31\right){y}={x}^{3}+\left(2a^{3}+3a^{2}-18a-16\right){x}^{2}+\left(525a^{3}+906a^{2}-4781a-5821\right){x}-16874a^{3}-29751a^{2}+154508a+189916$ |
| 55.1-c4 |
55.1-c |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.119930090$ |
$444.8207860$ |
6.940416381 |
\( -\frac{45227}{55} a^{3} - \frac{90454}{55} a^{2} + \frac{407043}{55} a + \frac{122986}{11} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 18\) , \( -2 a^{3} - 3 a^{2} + 17 a + 17\) , \( a^{3} + 2 a^{2} - 8 a - 12\) , \( 4 a^{3} + 11 a^{2} - 36 a - 71\) , \( -7 a^{3} - 13 a^{2} + 59 a + 82\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+18\right){x}{y}+\left(a^{3}+2a^{2}-8a-12\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+17a+17\right){x}^{2}+\left(4a^{3}+11a^{2}-36a-71\right){x}-7a^{3}-13a^{2}+59a+82$ |
| 55.1-c5 |
55.1-c |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \) |
$0.119930090$ |
$444.8207860$ |
6.940416381 |
\( -\frac{132583563}{605} a^{3} - \frac{265167126}{605} a^{2} + \frac{1193252067}{605} a + \frac{1889656801}{605} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 18\) , \( -2 a^{3} - 3 a^{2} + 17 a + 17\) , \( a^{3} + 2 a^{2} - 8 a - 12\) , \( -41 a^{3} - 49 a^{2} + 374 a + 199\) , \( -48 a^{3} - 236 a^{2} + 314 a + 1936\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+18\right){x}{y}+\left(a^{3}+2a^{2}-8a-12\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+17a+17\right){x}^{2}+\left(-41a^{3}-49a^{2}+374a+199\right){x}-48a^{3}-236a^{2}+314a+1936$ |
| 55.1-c6 |
55.1-c |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{12} \cdot 11^{12} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.119930090$ |
$49.42453178$ |
6.940416381 |
\( \frac{1485675267531}{221445125} a^{3} + \frac{2971350535062}{221445125} a^{2} - \frac{13371077407779}{221445125} a - \frac{15161713818194}{221445125} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 18\) , \( -2 a^{3} - 3 a^{2} + 17 a + 17\) , \( a^{3} + 2 a^{2} - 8 a - 12\) , \( -281 a^{3} - 414 a^{2} + 2529 a + 2069\) , \( 2439 a^{3} + 5562 a^{2} - 20594 a - 36710\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+18\right){x}{y}+\left(a^{3}+2a^{2}-8a-12\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+17a+17\right){x}^{2}+\left(-281a^{3}-414a^{2}+2529a+2069\right){x}+2439a^{3}+5562a^{2}-20594a-36710$ |
| 55.1-c7 |
55.1-c |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{24} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.479720362$ |
$3.089033236$ |
6.940416381 |
\( \frac{114278307303626907}{78460709418025} a^{3} + \frac{228556614607253814}{78460709418025} a^{2} - \frac{1028504765732642163}{78460709418025} a - \frac{256402923382212311}{15692141883605} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 18\) , \( -2 a^{3} - 3 a^{2} + 17 a + 17\) , \( a^{3} + 2 a^{2} - 8 a - 12\) , \( -656 a^{3} - 1364 a^{2} + 5629 a + 8619\) , \( -7806 a^{3} - 8813 a^{2} + 72241 a + 31630\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+18\right){x}{y}+\left(a^{3}+2a^{2}-8a-12\right){y}={x}^{3}+\left(-2a^{3}-3a^{2}+17a+17\right){x}^{2}+\left(-656a^{3}-1364a^{2}+5629a+8619\right){x}-7806a^{3}-8813a^{2}+72241a+31630$ |
| 55.1-c8 |
55.1-c |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{24} \cdot 11^{6} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$0.029982522$ |
$49.42453178$ |
6.940416381 |
\( \frac{4560282420936767}{20796875} a^{3} + \frac{9120564841873534}{20796875} a^{2} - \frac{41042541788430903}{20796875} a - \frac{51904810910436359}{20796875} \) |
\( \bigl[-3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 4 a^{3} + 7 a^{2} - 35 a - 44\) , \( a + 1\) , \( 1882 a^{3} + 2695 a^{2} - 16173 a - 19160\) , \( -41290 a^{3} - 49185 a^{2} + 337842 a + 388017\bigr] \) |
${y}^2+\left(-3a^{3}-5a^{2}+27a+30\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(4a^{3}+7a^{2}-35a-44\right){x}^{2}+\left(1882a^{3}+2695a^{2}-16173a-19160\right){x}-41290a^{3}-49185a^{2}+337842a+388017$ |
| 55.1-d1 |
55.1-d |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{6} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$394.0832472$ |
0.801088117 |
\( -\frac{754904381777}{33275} a^{3} - \frac{1509808763554}{33275} a^{2} + \frac{6794139435993}{33275} a + \frac{2056062822711}{6655} \) |
\( \bigl[a^{3} + 2 a^{2} - 8 a - 13\) , \( 0\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( -8 a^{3} + 123 a^{2} - 157 a - 357\) , \( -3732 a^{3} + 16567 a^{2} - 5287 a - 33114\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-8a-13\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(-8a^{3}+123a^{2}-157a-357\right){x}-3732a^{3}+16567a^{2}-5287a-33114$ |
| 55.1-d2 |
55.1-d |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$394.0832472$ |
0.801088117 |
\( -\frac{45227}{55} a^{3} - \frac{90454}{55} a^{2} + \frac{407043}{55} a + \frac{122986}{11} \) |
\( \bigl[a^{3} + 2 a^{2} - 8 a - 13\) , \( 0\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 7 a^{3} - 2 a^{2} - 37 a - 32\) , \( 141 a^{3} - 623 a^{2} + 195 a + 1240\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-8a-13\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(7a^{3}-2a^{2}-37a-32\right){x}+141a^{3}-623a^{2}+195a+1240$ |
| 55.1-d3 |
55.1-d |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$98.52081182$ |
0.801088117 |
\( -\frac{132583563}{605} a^{3} - \frac{265167126}{605} a^{2} + \frac{1193252067}{605} a + \frac{1889656801}{605} \) |
\( \bigl[a^{3} + 2 a^{2} - 8 a - 13\) , \( 0\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 112 a^{3} - 457 a^{2} + 93 a + 863\) , \( 4018 a^{3} - 17913 a^{2} + 5823 a + 35896\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-8a-13\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(112a^{3}-457a^{2}+93a+863\right){x}+4018a^{3}-17913a^{2}+5823a+35896$ |
| 55.1-d4 |
55.1-d |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$24.63020295$ |
0.801088117 |
\( -\frac{48555143354501}{275} a^{3} - \frac{97110286709002}{275} a^{2} + \frac{436996290190509}{275} a + \frac{661225593030336}{275} \) |
\( \bigl[a\) , \( 0\) , \( -2 a^{3} - 3 a^{2} + 18 a + 18\) , \( -7284 a^{3} - 13432 a^{2} + 63735 a + 79269\) , \( 74102 a^{3} + 136770 a^{2} - 648350 a - 807672\bigr] \) |
${y}^2+a{x}{y}+\left(-2a^{3}-3a^{2}+18a+18\right){y}={x}^{3}+\left(-7284a^{3}-13432a^{2}+63735a+79269\right){x}+74102a^{3}+136770a^{2}-648350a-807672$ |
| 55.1-d5 |
55.1-d |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{8} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$6.157550739$ |
0.801088117 |
\( \frac{626283905886387}{73205} a^{3} + \frac{1252567811772774}{73205} a^{2} - \frac{5636555152977483}{73205} a - \frac{1425668429911408}{14641} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 17\) , \( 0\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 257 a^{3} - 1074 a^{2} + 250 a + 2061\) , \( 14244 a^{3} - 63178 a^{2} + 20091 a + 126198\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+17\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(257a^{3}-1074a^{2}+250a+2061\right){x}+14244a^{3}-63178a^{2}+20091a+126198$ |
| 55.1-d6 |
55.1-d |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{12} \cdot 11^{12} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$98.52081182$ |
0.801088117 |
\( \frac{1485675267531}{221445125} a^{3} + \frac{2971350535062}{221445125} a^{2} - \frac{13371077407779}{221445125} a - \frac{15161713818194}{221445125} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 17\) , \( 0\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 167 a^{3} - 324 a^{2} - 470 a + 111\) , \( -3744 a^{3} + 15122 a^{2} - 2751 a - 28356\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+17\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(167a^{3}-324a^{2}-470a+111\right){x}-3744a^{3}+15122a^{2}-2751a-28356$ |
| 55.1-d7 |
55.1-d |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{6} \cdot 11^{24} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2^{2} \) |
$1$ |
$6.157550739$ |
0.801088117 |
\( \frac{114278307303626907}{78460709418025} a^{3} + \frac{228556614607253814}{78460709418025} a^{2} - \frac{1028504765732642163}{78460709418025} a - \frac{256402923382212311}{15692141883605} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 17\) , \( 0\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 167 a^{3} - 1374 a^{2} + 1305 a + 3561\) , \( 10041 a^{3} - 53878 a^{2} + 30019 a + 119474\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+17\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(167a^{3}-1374a^{2}+1305a+3561\right){x}+10041a^{3}-53878a^{2}+30019a+119474$ |
| 55.1-d8 |
55.1-d |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.1 |
\( 5 \cdot 11 \) |
\( 5^{24} \cdot 11^{6} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (a^3+2a^2-8a-11)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$24.63020295$ |
0.801088117 |
\( \frac{4560282420936767}{20796875} a^{3} + \frac{9120564841873534}{20796875} a^{2} - \frac{41042541788430903}{20796875} a - \frac{51904810910436359}{20796875} \) |
\( \bigl[-2 a^{3} - 3 a^{2} + 18 a + 17\) , \( 0\) , \( -3 a^{3} - 5 a^{2} + 27 a + 30\) , \( 1847 a^{3} - 6554 a^{2} - 165 a + 10981\) , \( -227469 a^{3} + 1029582 a^{2} - 355905 a - 2082866\bigr] \) |
${y}^2+\left(-2a^{3}-3a^{2}+18a+17\right){x}{y}+\left(-3a^{3}-5a^{2}+27a+30\right){y}={x}^{3}+\left(1847a^{3}-6554a^{2}-165a+10981\right){x}-227469a^{3}+1029582a^{2}-355905a-2082866$ |
| 55.2-a1 |
55.2-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{4} \cdot 11^{4} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (3a^3+5a^2-27a-32)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$1578.802794$ |
1.426388029 |
\( \frac{132583563}{605} a^{3} + \frac{265167126}{605} a^{2} - \frac{1193252067}{605} a - \frac{1424932274}{605} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 13\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( a^{3} + 2 a^{2} - 9 a - 13\) , \( 6 a^{3} + 12 a^{2} - 54 a - 83\) , \( -8 a^{3} - 16 a^{2} + 72 a + 109\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-13\right){x}{y}+\left(a^{3}+2a^{2}-9a-13\right){y}={x}^{3}+\left(a^{3}+2a^{2}-9a-12\right){x}^{2}+\left(6a^{3}+12a^{2}-54a-83\right){x}-8a^{3}-16a^{2}+72a+109$ |
| 55.2-a2 |
55.2-a |
$8$ |
$12$ |
4.4.15125.1 |
$4$ |
$[4, 0]$ |
55.2 |
\( 5 \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$18.13559$ |
$(-2a^3-3a^2+18a+19), (3a^3+5a^2-27a-32)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1578.802794$ |
1.426388029 |
\( \frac{45227}{55} a^{3} + \frac{90454}{55} a^{2} - \frac{407043}{55} a - \frac{103149}{11} \) |
\( \bigl[a^{3} + 2 a^{2} - 9 a - 13\) , \( a^{3} + 2 a^{2} - 9 a - 12\) , \( a^{3} + 2 a^{2} - 9 a - 13\) , \( a^{3} + 2 a^{2} - 9 a - 13\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}+2a^{2}-9a-13\right){x}{y}+\left(a^{3}+2a^{2}-9a-13\right){y}={x}^{3}+\left(a^{3}+2a^{2}-9a-12\right){x}^{2}+\left(a^{3}+2a^{2}-9a-13\right){x}$ |
*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.
