| 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 |
| 7.1-a1 |
7.1-a |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
7.1 |
\( 7 \) |
\( 7 \) |
$43.07540$ |
$(a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.016869327$ |
$10621.34098$ |
2.25769952 |
\( -\frac{329930}{7} a^{4} + \frac{1155976}{7} a^{3} - \frac{414375}{7} a^{2} - \frac{1026539}{7} a + \frac{216751}{7} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( -a^{4} + 3 a^{3} + a^{2} - 5 a\) , \( a\) , \( -a^{4} + 5 a^{3} + 3 a^{2} - 14 a + 3\) , \( -a^{4} + 7 a^{3} - 15 a + 3\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-5a\right){x}^{2}+\left(-a^{4}+5a^{3}+3a^{2}-14a+3\right){x}-a^{4}+7a^{3}-15a+3$ |
| 15.1-a1 |
15.1-a |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{3} \cdot 5^{3} \) |
$46.48669$ |
$(a-1), (a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 3 \) |
$1$ |
$224.5404955$ |
1.69759835 |
\( -\frac{24873245517867970931}{3375} a^{4} + \frac{2376486437763540037}{675} a^{3} + \frac{117581781067117554244}{3375} a^{2} + \frac{18208708644071157631}{1125} a - \frac{16338618945030013868}{3375} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 2 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( 19 a^{4} - 52 a^{3} - 141 a^{2} - 31 a + 3\) , \( 907 a^{4} - 92 a^{3} - 3463 a^{2} - 1594 a + 488\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-2a\right){x}^{2}+\left(19a^{4}-52a^{3}-141a^{2}-31a+3\right){x}+907a^{4}-92a^{3}-3463a^{2}-1594a+488$ |
| 15.1-a2 |
15.1-a |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{6} \cdot 5^{6} \) |
$46.48669$ |
$(a-1), (a^2-a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$898.1619820$ |
1.69759835 |
\( -\frac{359817232237948}{11390625} a^{4} + \frac{57997732463996}{2278125} a^{3} + \frac{1546246628330702}{11390625} a^{2} + \frac{119640549156923}{3796875} a - \frac{134798205542569}{11390625} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 2 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( 4 a^{4} - 17 a^{3} - 6 a^{2} + 34 a - 7\) , \( 29 a^{4} - 40 a^{3} - 91 a^{2} + 50 a - 6\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-2a\right){x}^{2}+\left(4a^{4}-17a^{3}-6a^{2}+34a-7\right){x}+29a^{4}-40a^{3}-91a^{2}+50a-6$ |
| 15.1-a3 |
15.1-a |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{3} \cdot 5^{3} \) |
$46.48669$ |
$(a-1), (a^2-a-2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 3 \) |
$1$ |
$3592.647928$ |
1.69759835 |
\( -\frac{529444}{3375} a^{4} - \frac{2834212}{675} a^{3} + \frac{27378131}{3375} a^{2} + \frac{12513494}{1125} a - \frac{9659257}{3375} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 2 a^{3} - a^{2} - 3 a - 1\) , \( 8 a^{4} - 13 a^{3} - 34 a^{2} + 30 a + 35\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+3\right){x}^{2}+\left(2a^{3}-a^{2}-3a-1\right){x}+8a^{4}-13a^{3}-34a^{2}+30a+35$ |
| 15.1-a4 |
15.1-a |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{12} \cdot 5^{12} \) |
$46.48669$ |
$(a-1), (a^2-a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$4$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$28.06756194$ |
1.69759835 |
\( -\frac{14650832330447075991521508547}{129746337890625} a^{4} + \frac{8256528281659217619012714869}{25949267578125} a^{3} + \frac{24843720611139878724348519428}{129746337890625} a^{2} - \frac{31190184237539435782753389553}{43248779296875} a + \frac{17915641814532777647241914084}{129746337890625} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 4 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( 41 a^{4} - 160 a^{3} + 103 a^{2} + 123 a - 82\) , \( -836 a^{4} + 2911 a^{3} - 1005 a^{2} - 2581 a + 476\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-4a+2\right){x}^{2}+\left(41a^{4}-160a^{3}+103a^{2}+123a-82\right){x}-836a^{4}+2911a^{3}-1005a^{2}-2581a+476$ |
| 15.1-b1 |
15.1-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{6} \cdot 5^{3} \) |
$46.48669$ |
$(a-1), (a^2-a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$121.9808439$ |
1.84442881 |
\( -\frac{815895463534687}{91125} a^{4} + \frac{571481037512924}{18225} a^{3} - \frac{1028729291749087}{91125} a^{2} - \frac{844716480359038}{30375} a + \frac{543144154205414}{91125} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( a^{3} - a^{2} - 2 a\) , \( a^{3} - a^{2} + 1\) , \( -20 a^{4} + 58 a^{3} + 33 a^{2} - 131 a + 23\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-2a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}^{2}+\left(a^{3}-a^{2}+1\right){x}-20a^{4}+58a^{3}+33a^{2}-131a+23$ |
| 15.1-c1 |
15.1-c |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{6} \cdot 5^{7} \) |
$46.48669$ |
$(a-1), (a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.001443994$ |
$5344.441995$ |
4.08419204 |
\( -\frac{5398822426327}{56953125} a^{4} + \frac{1938175503929}{11390625} a^{3} + \frac{23524238578148}{56953125} a^{2} - \frac{7382519325148}{18984375} a - \frac{26030781292756}{56953125} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 1\) , \( -a^{4} + 3 a^{3} + a^{2} - 6 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -4 a^{4} + 10 a^{3} + 9 a^{2} - 24 a + 2\) , \( -6 a^{4} + 17 a^{3} + 10 a^{2} - 38 a + 7\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+a^{2}-6a\right){x}^{2}+\left(-4a^{4}+10a^{3}+9a^{2}-24a+2\right){x}-6a^{4}+17a^{3}+10a^{2}-38a+7$ |
| 21.1-a1 |
21.1-a |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{24} \cdot 7 \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$193.1767287$ |
2.92095638 |
\( -\frac{1896851943293167140581098101982}{1977006755367} a^{4} + \frac{906186352204208922782720211388}{1977006755367} a^{3} + \frac{8966866507766977437448802136362}{1977006755367} a^{2} + \frac{1388572229495570270121438444647}{659002251789} a - \frac{1246069418430474811187328751336}{1977006755367} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{4} - 3 a^{3} - a^{2} + 5 a - 2\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 19 a^{4} - 70 a^{3} - 6 a^{2} + 163 a - 92\) , \( 81 a^{4} - 297 a^{3} - 15 a^{2} + 674 a - 375\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+5a-2\right){x}^{2}+\left(19a^{4}-70a^{3}-6a^{2}+163a-92\right){x}+81a^{4}-297a^{3}-15a^{2}+674a-375$ |
| 21.1-a2 |
21.1-a |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{6} \cdot 7 \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$3090.827659$ |
2.92095638 |
\( \frac{29167328623}{5103} a^{4} - \frac{52218562168}{5103} a^{3} - \frac{127632145232}{5103} a^{2} + \frac{39739460104}{1701} a + \frac{141578419168}{5103} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{4} - 3 a^{3} - a^{2} + 5 a - 2\) , \( a^{3} - 2 a^{2} - a + 2\) , \( -a^{4} + 9 a^{2} - 2 a - 12\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 5 a + 2\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+5a-2\right){x}^{2}+\left(-a^{4}+9a^{2}-2a-12\right){x}+a^{4}-3a^{3}-2a^{2}+5a+2$ |
| 21.1-a3 |
21.1-a |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{12} \cdot 7^{2} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$772.7069148$ |
2.92095638 |
\( -\frac{27529873963067788}{26040609} a^{4} + \frac{58660197781309168}{26040609} a^{3} + \frac{71188552285862849}{26040609} a^{2} - \frac{35483860372170136}{8680203} a + \frac{18470953759678016}{26040609} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{3} - a^{2} - 2 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( -25 a^{4} + 101 a^{3} - 74 a^{2} - 54 a + 11\) , \( -18 a^{4} + 75 a^{3} - 106 a^{2} + 89 a - 15\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a-1\right){x}^{2}+\left(-25a^{4}+101a^{3}-74a^{2}-54a+11\right){x}-18a^{4}+75a^{3}-106a^{2}+89a-15$ |
| 21.1-a4 |
21.1-a |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{6} \cdot 7^{4} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$24.14709108$ |
2.92095638 |
\( -\frac{5458306643706940647353374}{1750329} a^{4} + \frac{15380240339628053901985852}{1750329} a^{3} + \frac{9255763817904494438847722}{1750329} a^{2} - \frac{11620199520688236637384441}{583443} a + \frac{6674642615880646886804840}{1750329} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( a + 1\) , \( 40 a^{4} + 62 a^{3} - 390 a^{2} - 250 a + 74\) , \( -1080 a^{4} + 1094 a^{3} + 3555 a^{2} + 1121 a - 380\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+3\right){x}^{2}+\left(40a^{4}+62a^{3}-390a^{2}-250a+74\right){x}-1080a^{4}+1094a^{3}+3555a^{2}+1121a-380$ |
| 21.1-b1 |
21.1-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7^{5} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$936.4299988$ |
2.35990397 |
\( -\frac{8875725984047}{50421} a^{4} + \frac{15667660700996}{50421} a^{3} + \frac{39611664941314}{50421} a^{2} - \frac{12166694809578}{16807} a - \frac{43836213048548}{50421} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( -23 a^{4} + 20 a^{3} + 83 a^{2} - 48 a - 68\) , \( 16 a^{4} + 130 a^{3} + 60 a^{2} - 301 a - 226\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-23a^{4}+20a^{3}+83a^{2}-48a-68\right){x}+16a^{4}+130a^{3}+60a^{2}-301a-226$ |
| 21.1-c1 |
21.1-c |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{5} \cdot 7^{3} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.664985627$ |
$393.6056962$ |
3.29809113 |
\( -\frac{648785317343}{83349} a^{4} + \frac{2290474328822}{83349} a^{3} - \frac{854224433651}{83349} a^{2} - \frac{682459790885}{27783} a + \frac{439881942907}{83349} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( a^{3} - a^{2} - 4 a\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( -2 a^{4} + 5 a^{3} + 4 a^{2} - 9 a - 6\) , \( -2 a^{4} + 5 a^{3} + 2 a^{2} - 6 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-2a^{4}+5a^{3}+4a^{2}-9a-6\right){x}-2a^{4}+5a^{3}+2a^{2}-6a-3$ |
| 21.1-d1 |
21.1-d |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3^{21} \cdot 7 \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$759.8819357$ |
1.91498393 |
\( -\frac{5256937310936858}{73222472421} a^{4} + \frac{14830398855065063}{73222472421} a^{3} + \frac{8767524906200182}{73222472421} a^{2} - \frac{11097085144372877}{24407490807} a + \frac{6375517126310392}{73222472421} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 7 a + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -a^{3} - a^{2} + 7 a + 1\) , \( -2 a^{3} + 2 a^{2} + 3 a\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+7a+1\right){x}^{2}+\left(-a^{3}-a^{2}+7a+1\right){x}-2a^{3}+2a^{2}+3a$ |
| 21.1-e1 |
21.1-e |
$2$ |
$2$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{8} \cdot 7^{10} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$0.039242872$ |
$483.0862154$ |
4.77754132 |
\( -\frac{447869656933966912}{1853320108689} a^{4} - \frac{192859216712092367}{1853320108689} a^{3} + \frac{3017347598107239806}{1853320108689} a^{2} + \frac{583832562715713473}{617773369563} a - \frac{486851574748062709}{1853320108689} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 3 a^{3} - a^{2} + 5 a - 2\) , \( a^{2} - 1\) , \( -64 a^{4} - 34 a^{3} + 156 a^{2} + 82 a - 22\) , \( -1193 a^{4} - 701 a^{3} + 2941 a^{2} + 1659 a - 462\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+5a-2\right){x}^{2}+\left(-64a^{4}-34a^{3}+156a^{2}+82a-22\right){x}-1193a^{4}-701a^{3}+2941a^{2}+1659a-462$ |
| 21.1-e2 |
21.1-e |
$2$ |
$2$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{4} \cdot 7^{5} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.078485745$ |
$966.1724309$ |
4.77754132 |
\( -\frac{16648028282}{1361367} a^{4} + \frac{48971074091}{1361367} a^{3} + \frac{23240660581}{1361367} a^{2} - \frac{37083393329}{453789} a + \frac{30553814209}{1361367} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 3 a^{3} - a^{2} + 5 a - 2\) , \( a^{2} - 1\) , \( -4 a^{4} + a^{3} + 11 a^{2} - 3 a - 2\) , \( -33 a^{4} - 21 a^{3} + 82 a^{2} + 49 a - 14\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-3a^{3}-a^{2}+5a-2\right){x}^{2}+\left(-4a^{4}+a^{3}+11a^{2}-3a-2\right){x}-33a^{4}-21a^{3}+82a^{2}+49a-14$ |
| 21.1-f1 |
21.1-f |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{3} \cdot 7 \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$197.1519838$ |
1.49053240 |
\( -\frac{153070497856606}{189} a^{4} + \frac{536079052167229}{189} a^{3} - \frac{193000391621503}{189} a^{2} - \frac{158477636117107}{63} a + \frac{101899518874829}{189} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 6 a^{2} + 4 a + 5\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 13 a^{4} - 27 a^{3} - 48 a^{2} + 59 a + 50\) , \( 25 a^{4} - 46 a^{3} - 108 a^{2} + 107 a + 114\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4a+5\right){x}^{2}+\left(13a^{4}-27a^{3}-48a^{2}+59a+50\right){x}+25a^{4}-46a^{3}-108a^{2}+107a+114$ |
| 21.1-g1 |
21.1-g |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7^{7} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$579.2133566$ |
1.45967975 |
\( -\frac{528775071224}{2470629} a^{4} + \frac{950553956489}{2470629} a^{3} + \frac{2305240837483}{2470629} a^{2} - \frac{723642415159}{823543} a - \frac{2550579157220}{2470629} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( -4 a^{4} + 16 a^{3} - 5 a^{2} - 20 a + 1\) , \( 17 a^{4} - 57 a^{3} + 19 a^{2} + 49 a - 13\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+2a-2\right){x}^{2}+\left(-4a^{4}+16a^{3}-5a^{2}-20a+1\right){x}+17a^{4}-57a^{3}+19a^{2}+49a-13$ |
| 21.1-h1 |
21.1-h |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( 3 \cdot 7^{3} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.050744744$ |
$3811.829706$ |
2.43732575 |
\( \frac{5576440}{1029} a^{4} - \frac{17401336}{1029} a^{3} + \frac{1617925}{1029} a^{2} + \frac{5731185}{343} a - \frac{2362193}{1029} \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 3 a + 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( -2 a^{3} + 4 a^{2} + 8 a - 2\) , \( -2 a^{3} + 3 a^{2} + 7 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a+1\right){x}^{2}+\left(-2a^{3}+4a^{2}+8a-2\right){x}-2a^{3}+3a^{2}+7a-3$ |
| 21.1-i1 |
21.1-i |
$2$ |
$3$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{3} \cdot 7^{5} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$190.6753648$ |
1.44156707 |
\( \frac{20121994786004}{453789} a^{4} - \frac{56734097727800}{453789} a^{3} - \frac{34030017377563}{453789} a^{2} + \frac{42864004005068}{151263} a - \frac{24813991153717}{453789} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 3\) , \( -a^{4} + a^{3} + 4 a^{2} - a\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( -2 a^{4} + 2 a^{3} + 8 a^{2} + a - 4\) , \( -3 a^{4} + 8 a^{3} - a - 2\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a\right){x}^{2}+\left(-2a^{4}+2a^{3}+8a^{2}+a-4\right){x}-3a^{4}+8a^{3}-a-2$ |
| 21.1-i2 |
21.1-i |
$2$ |
$3$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
21.1 |
\( 3 \cdot 7 \) |
\( - 3^{9} \cdot 7^{15} \) |
$48.07745$ |
$(a-1), (a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{2} \) |
$1$ |
$63.55845496$ |
1.44156707 |
\( -\frac{2211923735912539047709}{93446253200208069} a^{4} - \frac{1367164368081460943588}{93446253200208069} a^{3} + \frac{5485724005817287250339}{93446253200208069} a^{2} + \frac{1059439780179054916553}{31148751066736023} a - \frac{841589631358527137218}{93446253200208069} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{3} - 2 a^{2} - a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( -2 a^{4} - a^{3} + 13 a^{2} + 15 a + 6\) , \( -43 a^{4} + 19 a^{3} + 204 a^{2} + 109 a - 17\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a+1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+3\right){x}^{2}+\left(-2a^{4}-a^{3}+13a^{2}+15a+6\right){x}-43a^{4}+19a^{3}+204a^{2}+109a-17$ |
| 27.1-a1 |
27.1-a |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$49.30102$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.031507788$ |
$7765.983225$ |
3.08321199 |
\( 217360 a^{4} - 98535 a^{3} - 1027091 a^{2} - 497750 a + 148146 \) |
\( \bigl[a\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 2 a + 1\) , \( a^{2} - a - 1\) , \( -3 a^{3} + a^{2} + 12 a - 2\) , \( 6 a^{4} - 18 a^{3} - 4 a^{2} + 34 a - 7\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-2a+1\right){x}^{2}+\left(-3a^{3}+a^{2}+12a-2\right){x}+6a^{4}-18a^{3}-4a^{2}+34a-7$ |
| 27.1-b1 |
27.1-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$49.30102$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.045776753$ |
$7429.772127$ |
4.28557898 |
\( -970261 a^{4} + 1761116 a^{3} + 4251688 a^{2} - 4024672 a - 4727026 \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a\) , \( a^{3} - 2 a^{2} - 2 a + 3\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 4 a - 4\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(a^{3}-2a^{2}-2a+3\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+2a\right){x}^{2}+\left(-2a^{4}+a^{3}+9a^{2}-4a-4\right){x}+a^{4}-2a^{3}-2a^{2}+3a$ |
| 27.1-c1 |
27.1-c |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$49.30102$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.008036300$ |
$13058.86186$ |
3.96708744 |
\( -970261 a^{4} + 1761116 a^{3} + 4251688 a^{2} - 4024672 a - 4727026 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( -13 a^{4} + 36 a^{2} + 3 a - 11\) , \( 45 a^{4} + 20 a^{3} - 113 a^{2} - 47 a + 23\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+1\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+4a-2\right){x}^{2}+\left(-13a^{4}+36a^{2}+3a-11\right){x}+45a^{4}+20a^{3}-113a^{2}-47a+23$ |
| 27.1-d1 |
27.1-d |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$49.30102$ |
$(a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3Ns |
$1$ |
\( 1 \) |
$0.071495737$ |
$2903.433709$ |
2.61565877 |
\( 217360 a^{4} - 98535 a^{3} - 1027091 a^{2} - 497750 a + 148146 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( 2 a^{4} - 6 a^{3} - 4 a^{2} + 15 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a+2\right){x}^{2}+\left(2a^{4}-6a^{3}-4a^{2}+15a+1\right){x}$ |
| 29.1-a1 |
29.1-a |
$2$ |
$3$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
29.1 |
\( 29 \) |
\( 29^{3} \) |
$49.65458$ |
$(-a^4+3a^3+2a^2-7a-1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.002340679$ |
$5998.902393$ |
2.65395769 |
\( \frac{162776978767113}{24389} a^{4} - \frac{459681019320279}{24389} a^{3} - \frac{274711571997669}{24389} a^{2} + \frac{1043325348186653}{24389} a - \frac{199864394175328}{24389} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 2 a - 2\) , \( a^{3} - a^{2} - 3 a\) , \( 5 a^{4} - 7 a^{3} - 24 a^{2} + 14 a + 19\) , \( 5 a^{4} - 11 a^{3} - 25 a^{2} + 33 a + 47\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){x}{y}+\left(a^{3}-a^{2}-3a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+2a-2\right){x}^{2}+\left(5a^{4}-7a^{3}-24a^{2}+14a+19\right){x}+5a^{4}-11a^{3}-25a^{2}+33a+47$ |
| 29.1-a2 |
29.1-a |
$2$ |
$3$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
29.1 |
\( 29 \) |
\( 29 \) |
$49.65458$ |
$(-a^4+3a^3+2a^2-7a-1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.002340679$ |
$17996.70718$ |
2.65395769 |
\( -\frac{1089948}{29} a^{4} + \frac{1864085}{29} a^{3} + \frac{4767546}{29} a^{2} - \frac{4257192}{29} a - \frac{5239864}{29} \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 6\) , \( a^{3} - 2 a^{2} - a + 3\) , \( 6 a^{4} - 11 a^{3} - 20 a^{2} + 23 a + 9\) , \( -3 a^{4} + 11 a^{3} + 2 a^{2} - 23 a + 10\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{3}-2a^{2}-a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+3a+6\right){x}^{2}+\left(6a^{4}-11a^{3}-20a^{2}+23a+9\right){x}-3a^{4}+11a^{3}+2a^{2}-23a+10$ |
| 29.2-a1 |
29.2-a |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$49.65458$ |
$(a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$785.1599122$ |
1.97868714 |
\( \frac{56056086528}{29} a^{4} - \frac{157952770048}{29} a^{3} - \frac{95055249408}{29} a^{2} + \frac{358012157952}{29} a - \frac{68549607424}{29} \) |
\( \bigl[0\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a + 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -18 a^{4} + 63 a^{3} - 23 a^{2} - 52 a + 8\) , \( -46 a^{4} + 162 a^{3} - 62 a^{2} - 139 a + 30\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+4a+3\right){x}^{2}+\left(-18a^{4}+63a^{3}-23a^{2}-52a+8\right){x}-46a^{4}+162a^{3}-62a^{2}-139a+30$ |
| 29.2-b1 |
29.2-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
29.2 |
\( 29 \) |
\( 29 \) |
$49.65458$ |
$(a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$868.0658240$ |
2.18761893 |
\( \frac{1401154}{29} a^{4} - \frac{3548305}{29} a^{3} - \frac{4956090}{29} a^{2} + \frac{12632525}{29} a - \frac{2366297}{29} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -a^{4} + 4 a^{3} - 8 a + 2\) , \( -a^{4} + 5 a^{3} - 2 a^{2} - 7 a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-5a\right){x}^{2}+\left(-a^{4}+4a^{3}-8a+2\right){x}-a^{4}+5a^{3}-2a^{2}-7a+1$ |
| 31.2-a1 |
31.2-a |
$2$ |
$2$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
31.2 |
\( 31 \) |
\( -31 \) |
$49.98684$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2717.210237$ |
1.71191526 |
\( -\frac{259194249}{31} a^{4} + \frac{122724988}{31} a^{3} + \frac{1226517608}{31} a^{2} + \frac{573377352}{31} a - \frac{171082836}{31} \) |
\( \bigl[a^{2} - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( a^{4} + 3 a^{3} - 14 a^{2} + 4 a + 2\) , \( 7 a^{4} - 29 a^{3} + 20 a^{2} + 34 a - 12\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+4a\right){x}^{2}+\left(a^{4}+3a^{3}-14a^{2}+4a+2\right){x}+7a^{4}-29a^{3}+20a^{2}+34a-12$ |
| 31.2-a2 |
31.2-a |
$2$ |
$2$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
31.2 |
\( 31 \) |
\( - 31^{2} \) |
$49.98684$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1358.605118$ |
1.71191526 |
\( -\frac{1361907057256}{961} a^{4} + \frac{3894266334280}{961} a^{3} + \frac{2351281224259}{961} a^{2} - \frac{8924919600994}{961} a + \frac{1713536968158}{961} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 8 a\) , \( a + 1\) , \( 39 a^{4} - 4 a^{3} - 213 a^{2} - 127 a + 35\) , \( -432 a^{4} + 189 a^{3} + 2066 a^{2} + 961 a - 287\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-8a\right){x}^{2}+\left(39a^{4}-4a^{3}-213a^{2}-127a+35\right){x}-432a^{4}+189a^{3}+2066a^{2}+961a-287$ |
| 32.1-a1 |
32.1-a |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{5} \) |
$50.14580$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.014837100$ |
$10988.68680$ |
2.05439454 |
\( \frac{14512359}{2} a^{4} - 13014914 a^{3} - \frac{63421617}{2} a^{2} + 29737221 a + \frac{70327249}{2} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{3} - 3 a^{2} + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( 7 a^{4} - 2 a^{3} - 19 a^{2} + 2 a + 11\) , \( 20 a^{4} + 9 a^{3} - 53 a^{2} - 20 a + 14\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}+5\right){x}^{2}+\left(7a^{4}-2a^{3}-19a^{2}+2a+11\right){x}+20a^{4}+9a^{3}-53a^{2}-20a+14$ |
| 32.1-b1 |
32.1-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{15} \) |
$50.14580$ |
$(2)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.001282380$ |
$18102.42945$ |
4.38766934 |
\( -\frac{385519}{8} a^{4} + 1487305 a^{3} - \frac{27634107}{8} a^{2} - \frac{26558261}{8} a + \frac{64582989}{8} \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 7 a^{4} - 16 a^{3} - 20 a^{2} + 38 a - 7\) , \( -8 a^{4} + 22 a^{3} + 19 a^{2} - 63 a + 12\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a+1\right){x}^{2}+\left(7a^{4}-16a^{3}-20a^{2}+38a-7\right){x}-8a^{4}+22a^{3}+19a^{2}-63a+12$ |
| 32.1-c1 |
32.1-c |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
32.1 |
\( 2^{5} \) |
\( 2^{5} \) |
$50.14580$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.017233524$ |
$9734.523264$ |
2.11386774 |
\( 468764391 a^{4} - 865910028 a^{3} - \frac{4136885951}{2} a^{2} + 1979303419 a + \frac{4637376449}{2} \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( 2 a^{4} - 10 a^{3} + 3 a^{2} + 23 a - 13\) , \( -5 a^{4} + 14 a^{3} + 6 a^{2} - 34 a + 17\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-1\right){x}^{2}+\left(2a^{4}-10a^{3}+3a^{2}+23a-13\right){x}-5a^{4}+14a^{3}+6a^{2}-34a+17$ |
| 35.1-a1 |
35.1-a |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{14} \cdot 7^{3} \) |
$50.59718$ |
$(a^2-a-2), (a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.041641950$ |
$230.6040931$ |
5.08202010 |
\( \frac{48380194396850948}{2093505859375} a^{4} + \frac{3606669228850629}{418701171875} a^{3} - \frac{117124669067695827}{2093505859375} a^{2} - \frac{43574211551344144}{2093505859375} a + \frac{14220687258387819}{2093505859375} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( a\) , \( 22 a^{4} - 9 a^{3} - 103 a^{2} - 48 a + 17\) , \( -660 a^{4} + 318 a^{3} + 3123 a^{2} + 1446 a - 437\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-3a-1\right){x}^{2}+\left(22a^{4}-9a^{3}-103a^{2}-48a+17\right){x}-660a^{4}+318a^{3}+3123a^{2}+1446a-437$ |
| 35.1-b1 |
35.1-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( 5^{2} \cdot 7^{7} \) |
$50.59718$ |
$(a^2-a-2), (a^2-2a-1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.000355888$ |
$11694.17036$ |
3.67088551 |
\( -\frac{25368698672623}{20588575} a^{4} + \frac{10458058575976}{4117715} a^{3} + \frac{87111373569102}{20588575} a^{2} - \frac{93187188010531}{20588575} a - \frac{108366183102969}{20588575} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( 4 a^{4} - 9 a^{3} - 16 a^{2} + 36 a - 9\) , \( -20 a^{4} + 51 a^{3} + 55 a^{2} - 149 a + 27\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a+2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+3a-1\right){x}^{2}+\left(4a^{4}-9a^{3}-16a^{2}+36a-9\right){x}-20a^{4}+51a^{3}+55a^{2}-149a+27$ |
| 39.1-a1 |
39.1-a |
$2$ |
$7$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3 \cdot 13^{14} \) |
$51.14769$ |
$(a-1), (a^3-2a^2-2a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.3 |
$2401$ |
\( 2 \) |
$1$ |
$0.159036179$ |
1.92458503 |
\( -\frac{106147976973931654958783038491665}{11812129157097867} a^{4} + \frac{190390459140008293205301433478108}{11812129157097867} a^{3} + \frac{463882315164982649215273549790629}{11812129157097867} a^{2} - \frac{145003213930959253658700173848522}{3937376385699289} a - \frac{514363770573996725110440127209515}{11812129157097867} \) |
\( \bigl[a^{2} - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( a^{3} - 2 a^{2} - a + 2\) , \( -54 a^{4} + 62 a^{3} + 347 a^{2} - 131 a - 618\) , \( -263 a^{4} - 511 a^{3} + 3742 a^{2} + 1200 a - 7529\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){x}^{2}+\left(-54a^{4}+62a^{3}+347a^{2}-131a-618\right){x}-263a^{4}-511a^{3}+3742a^{2}+1200a-7529$ |
| 39.1-a2 |
39.1-a |
$2$ |
$7$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{7} \cdot 13^{2} \) |
$51.14769$ |
$(a-1), (a^3-2a^2-2a+2)$ |
0 |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.1.1 |
$1$ |
\( 2 \cdot 7 \) |
$1$ |
$2672.921068$ |
1.92458503 |
\( \frac{1632496231}{369603} a^{4} - \frac{4695541873}{369603} a^{3} - \frac{2622520490}{369603} a^{2} + \frac{3591944890}{123201} a - \frac{2073797030}{369603} \) |
\( \bigl[a^{2} - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 6 a^{4} - 13 a^{3} - 13 a^{2} + 29 a + 2\) , \( -5 a^{4} + 20 a^{3} + 5 a^{2} - 44 a + 11\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-2a^{2}-a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){x}^{2}+\left(6a^{4}-13a^{3}-13a^{2}+29a+2\right){x}-5a^{4}+20a^{3}+5a^{2}-44a+11$ |
| 39.1-b1 |
39.1-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{7} \cdot 13 \) |
$51.14769$ |
$(a-1), (a^3-2a^2-2a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$236.3330466$ |
0.595584610 |
\( -\frac{3642000643702}{28431} a^{4} + \frac{6539754742459}{28431} a^{3} + \frac{15913923427616}{28431} a^{2} - \frac{4986737352736}{9477} a - \frac{17671147166671}{28431} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{4} + a^{3} + 6 a^{2} - 2 a - 6\) , \( 0\) , \( -5 a^{4} - 8 a^{3} + 11 a^{2} + 18 a + 5\) , \( -45 a^{4} - 25 a^{3} + 113 a^{2} + 59 a - 21\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-2a-6\right){x}^{2}+\left(-5a^{4}-8a^{3}+11a^{2}+18a+5\right){x}-45a^{4}-25a^{3}+113a^{2}+59a-21$ |
| 45.1-a1 |
45.1-a |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{12} \cdot 5^{7} \) |
$51.88488$ |
$(a-1), (a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 7 \) |
$0.046095473$ |
$625.4596807$ |
5.08598009 |
\( -\frac{5398822426327}{56953125} a^{4} + \frac{1938175503929}{11390625} a^{3} + \frac{23524238578148}{56953125} a^{2} - \frac{7382519325148}{18984375} a - \frac{26030781292756}{56953125} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -a^{2} + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 1\) , \( -5 a^{4} + 3 a^{3} + 9 a^{2} - 6 a + 3\) , \( 6 a^{4} + 11 a^{3} - 18 a^{2} - 24 a + 6\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-5a^{4}+3a^{3}+9a^{2}-6a+3\right){x}+6a^{4}+11a^{3}-18a^{2}-24a+6$ |
| 45.1-b1 |
45.1-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{12} \cdot 5^{3} \) |
$51.88488$ |
$(a-1), (a^2-a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.145192132$ |
$334.0606319$ |
3.66698093 |
\( -\frac{815895463534687}{91125} a^{4} + \frac{571481037512924}{18225} a^{3} - \frac{1028729291749087}{91125} a^{2} - \frac{844716480359038}{30375} a + \frac{543144154205414}{91125} \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 6 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -9 a^{4} + 9 a^{3} + 36 a^{2} + a - 4\) , \( -3 a^{4} + 3 a^{3} + 9 a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+2a^{2}-6a-1\right){x}^{2}+\left(-9a^{4}+9a^{3}+36a^{2}+a-4\right){x}-3a^{4}+3a^{3}+9a^{2}-5a-3$ |
| 45.1-c1 |
45.1-c |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{9} \cdot 5^{3} \) |
$51.88488$ |
$(a-1), (a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \cdot 3 \) |
$0.077362989$ |
$2922.932447$ |
4.27397817 |
\( -\frac{24873245517867970931}{3375} a^{4} + \frac{2376486437763540037}{675} a^{3} + \frac{117581781067117554244}{3375} a^{2} + \frac{18208708644071157631}{1125} a - \frac{16338618945030013868}{3375} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( -873 a^{4} + 1519 a^{3} + 3798 a^{2} - 3459 a - 4192\) , \( 21212 a^{4} - 37701 a^{3} - 92518 a^{2} + 86135 a + 102371\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+8a+2\right){x}^{2}+\left(-873a^{4}+1519a^{3}+3798a^{2}-3459a-4192\right){x}+21212a^{4}-37701a^{3}-92518a^{2}+86135a+102371$ |
| 45.1-c2 |
45.1-c |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{12} \cdot 5^{6} \) |
$51.88488$ |
$(a-1), (a^2-a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.038681494$ |
$5845.864894$ |
4.27397817 |
\( -\frac{359817232237948}{11390625} a^{4} + \frac{57997732463996}{2278125} a^{3} + \frac{1546246628330702}{11390625} a^{2} + \frac{119640549156923}{3796875} a - \frac{134798205542569}{11390625} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( -48 a^{4} + 74 a^{3} + 228 a^{2} - 164 a - 267\) , \( 216 a^{4} - 355 a^{3} - 1026 a^{2} + 818 a + 1240\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+8a+2\right){x}^{2}+\left(-48a^{4}+74a^{3}+228a^{2}-164a-267\right){x}+216a^{4}-355a^{3}-1026a^{2}+818a+1240$ |
| 45.1-c3 |
45.1-c |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( - 3^{9} \cdot 5^{3} \) |
$51.88488$ |
$(a-1), (a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.019340747$ |
$5845.864894$ |
4.27397817 |
\( -\frac{529444}{3375} a^{4} - \frac{2834212}{675} a^{3} + \frac{27378131}{3375} a^{2} + \frac{12513494}{1125} a - \frac{9659257}{3375} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 4 a - 7\) , \( 3 a^{4} - 6 a^{3} - 14 a^{2} + 19 a + 24\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+8a+2\right){x}^{2}+\left(-3a^{4}+4a^{3}+13a^{2}-4a-7\right){x}+3a^{4}-6a^{3}-14a^{2}+19a+24$ |
| 45.1-c4 |
45.1-c |
$4$ |
$4$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
45.1 |
\( 3^{2} \cdot 5 \) |
\( 3^{18} \cdot 5^{12} \) |
$51.88488$ |
$(a-1), (a^2-a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2^{4} \cdot 3 \) |
$0.077362989$ |
$365.3665558$ |
4.27397817 |
\( -\frac{14650832330447075991521508547}{129746337890625} a^{4} + \frac{8256528281659217619012714869}{25949267578125} a^{3} + \frac{24843720611139878724348519428}{129746337890625} a^{2} - \frac{31190184237539435782753389553}{43248779296875} a + \frac{17915641814532777647241914084}{129746337890625} \) |
\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{4} + a^{3} + 4 a^{2} - a\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 76 a^{4} - 252 a^{3} + 10 a^{2} + 380 a - 103\) , \( 484 a^{4} - 1841 a^{3} + 1231 a^{2} + 822 a - 196\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a\right){x}^{2}+\left(76a^{4}-252a^{3}+10a^{2}+380a-103\right){x}+484a^{4}-1841a^{3}+1231a^{2}+822a-196$ |
| 49.1-a1 |
49.1-a |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{8} \) |
$52.32860$ |
$(a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.023040375$ |
$3270.210192$ |
2.84823287 |
\( -56234000 a^{4} + 158453568 a^{3} + 95361498 a^{2} - 359148967 a + 68749009 \) |
\( \bigl[a\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 38 a^{4} - 109 a^{3} - 61 a^{2} + 246 a - 53\) , \( -198 a^{4} + 556 a^{3} + 338 a^{2} - 1260 a + 238\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-2a-2\right){x}^{2}+\left(38a^{4}-109a^{3}-61a^{2}+246a-53\right){x}-198a^{4}+556a^{3}+338a^{2}-1260a+238$ |
| 49.1-b1 |
49.1-b |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{2} \) |
$52.32860$ |
$(a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$981.1054049$ |
2.47249079 |
\( -56234000 a^{4} + 158453568 a^{3} + 95361498 a^{2} - 359148967 a + 68749009 \) |
\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 2 a^{4} - 5 a^{3} - 7 a^{2} + 18 a - 3\) , \( -6 a^{4} + 18 a^{3} + 6 a^{2} - 34 a + 5\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-2a+2\right){x}{y}+\left(a^{3}-2a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(2a^{4}-5a^{3}-7a^{2}+18a-3\right){x}-6a^{4}+18a^{3}+6a^{2}-34a+5$ |
| 49.1-c1 |
49.1-c |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{2} \) |
$52.32860$ |
$(a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$472.6093456$ |
1.19102621 |
\( 33670706 a^{4} + 5034437 a^{3} - 114531811 a^{2} - 58113797 a + 16765677 \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a - 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 3 a^{4} - 8 a^{3} - 5 a^{2} + 15 a - 3\) , \( -2 a^{4} + 5 a^{3} + 3 a^{2} - 11 a + 2\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+4a+1\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-2a^{2}+3a-2\right){x}^{2}+\left(3a^{4}-8a^{3}-5a^{2}+15a-3\right){x}-2a^{4}+5a^{3}+3a^{2}-11a+2$ |
| 49.1-d1 |
49.1-d |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{8} \) |
$52.32860$ |
$(a^2-2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.116141978$ |
$3976.793183$ |
5.81984266 |
\( 33670706 a^{4} + 5034437 a^{3} - 114531811 a^{2} - 58113797 a + 16765677 \) |
\( \bigl[1\) , \( -a^{4} + 3 a^{3} - 5 a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( 4 a^{4} - 15 a^{3} + 5 a^{2} + 16 a - 3\) , \( 3 a^{4} - 7 a^{3} - 5 a^{2} + 16 a - 6\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(-a^{4}+3a^{3}-5a+3\right){x}^{2}+\left(4a^{4}-15a^{3}+5a^{2}+16a-3\right){x}+3a^{4}-7a^{3}-5a^{2}+16a-6$ |
| 49.1-e1 |
49.1-e |
$1$ |
$1$ |
5.5.157457.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{7} \) |
$52.32860$ |
$(a^2-2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$497.1360058$ |
2.50567205 |
\( -\frac{329930}{7} a^{4} + \frac{1155976}{7} a^{3} - \frac{414375}{7} a^{2} - \frac{1026539}{7} a + \frac{216751}{7} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 8 a\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 3\) , \( 3 a^{3} - a^{2} - 6 a + 1\) , \( -5 a^{4} + 19 a^{3} + 7 a^{2} - 44 a + 6\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+3\right){y}={x}^{3}+\left(a^{4}-3a^{3}-2a^{2}+8a\right){x}^{2}+\left(3a^{3}-a^{2}-6a+1\right){x}-5a^{4}+19a^{3}+7a^{2}-44a+6$ |
*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.
