| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 1.1-a1 |
1.1-a |
$1$ |
$1$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
1.1 |
\( 1 \) |
\( -1 \) |
$38.02299$ |
$\textsf{none}$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
|
|
$1$ |
\( 1 \) |
$0.004669130$ |
$23144.18203$ |
1.26981426 |
\( -190177 a^{4} - 60439 a^{3} + 567776 a^{2} + 46101 a - 237069 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - 5 a^{2} - 2 a + 3\) , \( -37 a^{4} + 51 a^{3} + 179 a^{2} - 142 a - 161\) , \( 195 a^{4} - 258 a^{3} - 952 a^{2} + 720 a + 871\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-5a^{2}-2a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-37a^{4}+51a^{3}+179a^{2}-142a-161\right){x}+195a^{4}-258a^{3}-952a^{2}+720a+871$ |
| 3.1-a1 |
3.1-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{24} \) |
$42.43834$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.812005243$ |
$148.4263714$ |
2.83244995 |
\( -\frac{13909502206453673}{282429536481} a^{4} - \frac{1763070073209710}{282429536481} a^{3} + \frac{46177073716740683}{282429536481} a^{2} - \frac{5084633849682476}{282429536481} a - \frac{24374755743159292}{282429536481} \) |
\( \bigl[a^{2} - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{2} - 2\) , \( -12 a^{4} + a^{3} + 49 a^{2} - 14 a - 31\) , \( -47 a^{4} - 35 a^{3} + 134 a^{2} + 48 a - 37\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(-12a^{4}+a^{3}+49a^{2}-14a-31\right){x}-47a^{4}-35a^{3}+134a^{2}+48a-37$ |
| 3.1-a2 |
3.1-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{8} \) |
$42.43834$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.270668414$ |
$445.2791144$ |
2.83244995 |
\( \frac{18791395}{6561} a^{4} - \frac{46775609}{6561} a^{3} - \frac{64267114}{6561} a^{2} + \frac{200069449}{6561} a - \frac{85285348}{6561} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( -a^{4} + 7 a^{2} - 7\) , \( 1\) , \( -3 a^{4} + 18 a^{2} + 6 a - 6\) , \( -5 a^{4} + 3 a^{3} + 26 a^{2} - 2 a - 13\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+7a^{2}-7\right){x}^{2}+\left(-3a^{4}+18a^{2}+6a-6\right){x}-5a^{4}+3a^{3}+26a^{2}-2a-13$ |
| 3.1-b1 |
3.1-b |
$4$ |
$15$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{15} \) |
$42.43834$ |
$(a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 3 \cdot 5 \) |
$1$ |
$904.2432468$ |
1.27505484 |
\( \frac{2163205707019}{14348907} a^{4} - \frac{1333206771227}{14348907} a^{3} - \frac{10398234681607}{14348907} a^{2} + \frac{770050568842}{14348907} a + \frac{4917305940221}{14348907} \) |
\( \bigl[a^{4} - 6 a^{2} - a + 5\) , \( a^{3} - a^{2} - 3 a\) , \( a^{2} - a - 2\) , \( 3 a^{4} - a^{3} - 15 a^{2} - 3 a + 11\) , \( 9 a^{4} - 13 a^{3} - 32 a^{2} + 33 a - 7\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-a+5\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(3a^{4}-a^{3}-15a^{2}-3a+11\right){x}+9a^{4}-13a^{3}-32a^{2}+33a-7$ |
| 3.1-b2 |
3.1-b |
$4$ |
$15$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{5} \) |
$42.43834$ |
$(a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$2712.729740$ |
1.27505484 |
\( -\frac{5373209408}{243} a^{4} + \frac{20352909778}{243} a^{3} - \frac{14879247598}{243} a^{2} - \frac{11060236445}{243} a + \frac{9038646761}{243} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( -2 a^{4} + 2 a^{3} + 9 a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}-a^{3}-4a^{2}+a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(-2a^{4}+2a^{3}+9a^{2}-2a-3\right){x}+a^{3}-a^{2}-3a+2$ |
| 3.1-b3 |
3.1-b |
$4$ |
$15$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$42.43834$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$0.868073517$ |
1.27505484 |
\( \frac{196431980923485032043748}{3} a^{4} - \frac{261734120708887776515612}{3} a^{3} - \frac{960450764303319125606275}{3} a^{2} + \frac{733866782073149257368763}{3} a + \frac{882762980096246220761624}{3} \) |
\( \bigl[a\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( 198 a^{4} - 143 a^{3} - 906 a^{2} + 113 a + 312\) , \( 2627 a^{4} - 1604 a^{3} - 12423 a^{2} + 617 a + 5042\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}-a^{3}-4a^{2}+a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-2\right){x}^{2}+\left(198a^{4}-143a^{3}-906a^{2}+113a+312\right){x}+2627a^{4}-1604a^{3}-12423a^{2}+617a+5042$ |
| 3.1-b4 |
3.1-b |
$4$ |
$15$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{3} \) |
$42.43834$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$625$ |
\( 3 \) |
$1$ |
$0.289357839$ |
1.27505484 |
\( \frac{1000614916168571896640282053132}{27} a^{4} - \frac{551928657809343736408840425008}{27} a^{3} - \frac{4801878940854530431361252615737}{27} a^{2} + \frac{49212422778026846134739081338}{27} a + \frac{2072509623374695331301701401601}{27} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 4\) , \( -a^{4} + a^{3} + 6 a^{2} - 3 a - 6\) , \( a^{3} - 3 a - 1\) , \( -490 a^{4} + 83 a^{3} + 1023 a^{2} + 17 a - 386\) , \( -21019 a^{4} + 2851 a^{3} + 48215 a^{2} + 241 a - 18326\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+4\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-3a-6\right){x}^{2}+\left(-490a^{4}+83a^{3}+1023a^{2}+17a-386\right){x}-21019a^{4}+2851a^{3}+48215a^{2}+241a-18326$ |
| 3.1-c1 |
3.1-c |
$1$ |
$1$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$42.43834$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.005265565$ |
$20055.56579$ |
1.24091577 |
\( \frac{3993811}{3} a^{4} - \frac{2195006}{3} a^{3} - \frac{19267171}{3} a^{2} + \frac{441772}{3} a + \frac{8156348}{3} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{4} + 5 a^{2} + 2 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -5 a^{4} + 7 a^{3} + 15 a^{2} - 5 a - 6\) , \( -a^{4} - 7 a^{3} + 22 a^{2} + 5 a - 13\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-2\right){x}^{2}+\left(-5a^{4}+7a^{3}+15a^{2}-5a-6\right){x}-a^{4}-7a^{3}+22a^{2}+5a-13$ |
| 3.2-a1 |
3.2-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{4} \) |
$42.43834$ |
$(a^4-a^3-5a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.012767095$ |
$4554.102319$ |
1.36642948 |
\( \frac{836279}{81} a^{4} - \frac{830812}{27} a^{3} - \frac{1182530}{81} a^{2} + \frac{7789456}{81} a - \frac{1678871}{27} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 5\) , \( a^{4} - 4 a^{3} + 2 a^{2} + 3 a + 1\) , \( 3 a^{4} - 15 a^{3} + 19 a^{2} + 4 a - 13\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+3\right){x}^{2}+\left(a^{4}-4a^{3}+2a^{2}+3a+1\right){x}+3a^{4}-15a^{3}+19a^{2}+4a-13$ |
| 3.2-a2 |
3.2-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{12} \) |
$42.43834$ |
$(a^4-a^3-5a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.038301285$ |
$1518.034106$ |
1.36642948 |
\( -\frac{33190771}{531441} a^{4} - \frac{40457941}{177147} a^{3} - \frac{149140862}{531441} a^{2} + \frac{390143776}{531441} a + \frac{255680749}{177147} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{4} - 6 a^{2} - a + 5\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( a^{3} - 2 a^{2} + a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{4}-6a^{2}-a+5\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-a^{3}+2a^{2}+4a\right){x}+a^{3}-2a^{2}+a$ |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$3651.921049$ |
2.14562454 |
\( -\frac{11813194}{3} a^{4} + \frac{15728116}{3} a^{3} + \frac{57768352}{3} a^{2} - 14697515 a - \frac{53061091}{3} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{3} - 2 a^{2} - a + 4\) , \( a^{3} - 3 a - 1\) , \( a^{4} - a^{3} + 3 a + 1\) , \( a^{4} + 2 a^{3} - 2 a^{2} - 1\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+4\right){x}^{2}+\left(a^{4}-a^{3}+3a+1\right){x}+a^{4}+2a^{3}-2a^{2}-1$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$1$ |
$1217.307016$ |
2.14562454 |
\( -\frac{59891263}{27} a^{4} + \frac{161384827}{27} a^{3} + \frac{124133809}{27} a^{2} - \frac{167286020}{9} a + \frac{243585233}{27} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{4} - 6 a^{2} - a + 5\) , \( -26 a^{4} + 34 a^{3} + 126 a^{2} - 93 a - 112\) , \( -7580 a^{4} + 10100 a^{3} + 37062 a^{2} - 28318 a - 34066\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+4\right){x}{y}+\left(a^{4}-6a^{2}-a+5\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a\right){x}^{2}+\left(-26a^{4}+34a^{3}+126a^{2}-93a-112\right){x}-7580a^{4}+10100a^{3}+37062a^{2}-28318a-34066$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$304.3267541$ |
2.14562454 |
\( -\frac{11753188106743147}{243} a^{4} + \frac{96079429918919450}{729} a^{3} + \frac{23796176143109479}{243} a^{2} - \frac{298567797356809406}{729} a + \frac{145918106790916558}{729} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( -a^{4} + 7 a^{2} - a - 6\) , \( a^{4} - 6 a^{2} + 6\) , \( -10 a^{4} + 18 a^{3} + 32 a^{2} - 31 a - 29\) , \( -12 a^{4} + 44 a^{3} - 14 a^{2} - 51 a - 12\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+2\right){x}{y}+\left(a^{4}-6a^{2}+6\right){y}={x}^{3}+\left(-a^{4}+7a^{2}-a-6\right){x}^{2}+\left(-10a^{4}+18a^{3}+32a^{2}-31a-29\right){x}-12a^{4}+44a^{3}-14a^{2}-51a-12$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{4} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$912.9802623$ |
2.14562454 |
\( 71363125510173 a^{4} - \frac{855784851374215}{9} a^{3} - 348928712573076 a^{2} + \frac{2399503497035677}{9} a + \frac{2886344938560904}{9} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{3} - 2 a^{2} - a + 4\) , \( a^{3} - 3 a - 1\) , \( a^{4} - 11 a^{3} + 5 a^{2} + 33 a - 19\) , \( a^{4} - 40 a^{3} + 17 a^{2} + 123 a - 80\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-a+4\right){x}^{2}+\left(a^{4}-11a^{3}+5a^{2}+33a-19\right){x}+a^{4}-40a^{3}+17a^{2}+123a-80$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$2558.894599$ |
1.50343531 |
\( -\frac{185589854444}{1594323} a^{4} + \frac{33512075785}{531441} a^{3} + \frac{897300267008}{1594323} a^{2} - \frac{15874024003}{1594323} a - \frac{127440080770}{531441} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{4} - a^{3} - 6 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{3} - 13 a^{2} + 7 a + 13\) , \( 2 a^{4} + 14 a^{3} - 32 a^{2} - 3 a + 19\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4a+6\right){x}^{2}+\left(a^{3}-13a^{2}+7a+13\right){x}+2a^{4}+14a^{3}-32a^{2}-3a+19$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{28} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$639.7236499$ |
1.50343531 |
\( -\frac{9643394282027486678}{2541865828329} a^{4} + \frac{8957775525551943043}{847288609443} a^{3} + \frac{19281214694345097116}{2541865828329} a^{2} - \frac{83352539984217702400}{2541865828329} a + \frac{13687544254216593458}{847288609443} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{4} + 6 a^{2} + a - 6\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -10 a^{4} + 33 a^{2} - 7 a - 15\) , \( 37 a^{4} + 17 a^{3} - 109 a^{2} - 14 a + 41\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-6\right){x}^{2}+\left(-10a^{4}+33a^{2}-7a-15\right){x}+37a^{4}+17a^{3}-109a^{2}-14a+41$ |
| 9.1-c1 |
9.1-c |
$4$ |
$4$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{31} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 7 \) |
$0.076174473$ |
$224.8028689$ |
4.22564444 |
\( \frac{23528616372387310155348371}{22876792454961} a^{4} - \frac{89094465321390947073627637}{22876792454961} a^{3} + \frac{65065606781630428155559141}{22876792454961} a^{2} + \frac{48451040387946407286293738}{22876792454961} a - \frac{39507407995806247013574710}{22876792454961} \) |
\( \bigl[a^{2} - 1\) , \( -a^{4} + 5 a^{2} + 3 a - 3\) , \( a + 1\) , \( -2518 a^{4} + 3350 a^{3} + 12308 a^{2} - 9389 a - 11301\) , \( -105027 a^{4} + 139938 a^{3} + 513525 a^{2} - 392365 a - 471979\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+3a-3\right){x}^{2}+\left(-2518a^{4}+3350a^{3}+12308a^{2}-9389a-11301\right){x}-105027a^{4}+139938a^{3}+513525a^{2}-392365a-471979$ |
| 9.1-c2 |
9.1-c |
$4$ |
$4$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{20} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \cdot 7 \) |
$0.038087236$ |
$1798.422951$ |
4.22564444 |
\( \frac{289876034537}{4782969} a^{4} - \frac{2000730083710}{4782969} a^{3} + \frac{3814114508431}{4782969} a^{2} - \frac{1391444238889}{4782969} a - \frac{220812972785}{4782969} \) |
\( \bigl[a^{2} - 1\) , \( -a^{4} + 5 a^{2} + 3 a - 3\) , \( a + 1\) , \( -183 a^{4} + 240 a^{3} + 893 a^{2} - 669 a - 811\) , \( -1214 a^{4} + 1611 a^{3} + 5930 a^{2} - 4516 a - 5440\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+3a-3\right){x}^{2}+\left(-183a^{4}+240a^{3}+893a^{2}-669a-811\right){x}-1214a^{4}+1611a^{3}+5930a^{2}-4516a-5440$ |
| 9.1-c3 |
9.1-c |
$4$ |
$4$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \cdot 7 \) |
$0.019043618$ |
$3596.845903$ |
4.22564444 |
\( -\frac{407561}{2187} a^{4} + \frac{37105}{2187} a^{3} + \frac{2315240}{2187} a^{2} - \frac{1082642}{2187} a + \frac{2216858}{2187} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a^{4} - 6 a^{2} + 5\) , \( a^{4} - a^{3} - 6 a^{2} + 4 a + 3\) , \( a^{3} - 2 a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{4}-6a^{2}+5\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(a^{4}-a^{3}-6a^{2}+4a+3\right){x}+a^{3}-2a^{2}-a-1$ |
| 9.1-c4 |
9.1-c |
$4$ |
$4$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{19} \) |
$47.36641$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \cdot 7 \) |
$0.076174473$ |
$224.8028689$ |
4.22564444 |
\( -\frac{34495656525909971}{531441} a^{4} + \frac{28517667503038951}{177147} a^{3} + \frac{81066375780822875}{531441} a^{2} - \frac{258890063675704426}{531441} a + \frac{39365969687406722}{177147} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a^{4} - 6 a^{2} + 5\) , \( 101 a^{4} - 116 a^{3} - 431 a^{2} + 294 a + 13\) , \( 375 a^{4} + 199 a^{3} - 2218 a^{2} - 1897 a + 2119\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{4}-6a^{2}+5\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-3\right){x}^{2}+\left(101a^{4}-116a^{3}-431a^{2}+294a+13\right){x}+375a^{4}+199a^{3}-2218a^{2}-1897a+2119$ |
| 9.2-a1 |
9.2-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{30} \) |
$47.36641$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$31.18022993$ |
1.31899807 |
\( -\frac{13909502206453673}{282429536481} a^{4} - \frac{1763070073209710}{282429536481} a^{3} + \frac{46177073716740683}{282429536481} a^{2} - \frac{5084633849682476}{282429536481} a - \frac{24374755743159292}{282429536481} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 2 a^{2} + 3 a - 3\) , \( a^{3} - 4 a - 1\) , \( -8 a^{4} + 28 a^{3} + 17 a^{2} - 91 a + 42\) , \( -2 a^{4} + 19 a^{3} - 66 a + 35\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-3\right){x}^{2}+\left(-8a^{4}+28a^{3}+17a^{2}-91a+42\right){x}-2a^{4}+19a^{3}-66a+35$ |
| 9.2-a2 |
9.2-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{14} \) |
$47.36641$ |
$(a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2525.598624$ |
1.31899807 |
\( \frac{18791395}{6561} a^{4} - \frac{46775609}{6561} a^{3} - \frac{64267114}{6561} a^{2} + \frac{200069449}{6561} a - \frac{85285348}{6561} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{4} + 7 a^{2} - a - 7\) , \( a^{3} - 3 a\) , \( -6 a^{4} - 2 a^{3} + 35 a^{2} + 11 a - 12\) , \( -13 a^{4} + 5 a^{3} + 69 a^{2} - 4 a - 34\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(-a^{4}+7a^{2}-a-7\right){x}^{2}+\left(-6a^{4}-2a^{3}+35a^{2}+11a-12\right){x}-13a^{4}+5a^{3}+69a^{2}-4a-34$ |
| 9.2-b1 |
9.2-b |
$1$ |
$1$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{3} \) |
$47.36641$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.019818171$ |
$5596.899110$ |
2.60677413 |
\( 59073422 a^{4} - 83449337 a^{3} - 279091818 a^{2} + 236795571 a + 236106333 \) |
\( \bigl[a^{4} - 6 a^{2} - a + 5\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a\) , \( -18 a^{4} + 8 a^{3} + 89 a^{2} + 7 a - 42\) , \( 518 a^{4} - 284 a^{3} - 2488 a^{2} + 19 a + 1078\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-a+5\right){x}{y}+a{y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}^{2}+\left(-18a^{4}+8a^{3}+89a^{2}+7a-42\right){x}+518a^{4}-284a^{3}-2488a^{2}+19a+1078$ |
| 9.2-c1 |
9.2-c |
$4$ |
$15$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{21} \) |
$47.36641$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$231.7007347$ |
2.17810967 |
\( \frac{2163205707019}{14348907} a^{4} - \frac{1333206771227}{14348907} a^{3} - \frac{10398234681607}{14348907} a^{2} + \frac{770050568842}{14348907} a + \frac{4917305940221}{14348907} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{3} - 5 a\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( -6 a^{4} + 11 a^{3} + 31 a^{2} - 33 a - 30\) , \( -11 a^{4} + 17 a^{3} + 55 a^{2} - 48 a - 51\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-6a^{4}+11a^{3}+31a^{2}-33a-30\right){x}-11a^{4}+17a^{3}+55a^{2}-48a-51$ |
| 9.2-c2 |
9.2-c |
$4$ |
$15$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{11} \) |
$47.36641$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$231.7007347$ |
2.17810967 |
\( -\frac{5373209408}{243} a^{4} + \frac{20352909778}{243} a^{3} - \frac{14879247598}{243} a^{2} - \frac{11060236445}{243} a + \frac{9038646761}{243} \) |
\( \bigl[a^{4} - 6 a^{2} + 5\) , \( -a^{4} + 5 a^{2} + 2 a - 4\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -51 a^{4} + 65 a^{3} + 246 a^{2} - 174 a - 218\) , \( 240 a^{4} - 322 a^{3} - 1177 a^{2} + 911 a + 1088\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}+5\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+2a-4\right){x}^{2}+\left(-51a^{4}+65a^{3}+246a^{2}-174a-218\right){x}+240a^{4}-322a^{3}-1177a^{2}+911a+1088$ |
| 9.2-c3 |
9.2-c |
$4$ |
$15$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{7} \) |
$47.36641$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$9.268029391$ |
2.17810967 |
\( \frac{196431980923485032043748}{3} a^{4} - \frac{261734120708887776515612}{3} a^{3} - \frac{960450764303319125606275}{3} a^{2} + \frac{733866782073149257368763}{3} a + \frac{882762980096246220761624}{3} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 4\) , \( a^{4} - a^{3} - 6 a^{2} + 4 a + 5\) , \( a^{4} - 6 a^{2} + 6\) , \( -315 a^{4} + 323 a^{3} + 1794 a^{2} - 1158 a - 1686\) , \( 4230 a^{4} - 4218 a^{3} - 25266 a^{2} + 16670 a + 23055\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+4\right){x}{y}+\left(a^{4}-6a^{2}+6\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+4a+5\right){x}^{2}+\left(-315a^{4}+323a^{3}+1794a^{2}-1158a-1686\right){x}+4230a^{4}-4218a^{3}-25266a^{2}+16670a+23055$ |
| 9.2-c4 |
9.2-c |
$4$ |
$15$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$47.36641$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3, 5$ |
3B, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$9.268029391$ |
2.17810967 |
\( \frac{1000614916168571896640282053132}{27} a^{4} - \frac{551928657809343736408840425008}{27} a^{3} - \frac{4801878940854530431361252615737}{27} a^{2} + \frac{49212422778026846134739081338}{27} a + \frac{2072509623374695331301701401601}{27} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{3} - 5 a\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( -391 a^{4} + 521 a^{3} + 2086 a^{2} - 1593 a - 2550\) , \( 12311 a^{4} - 14868 a^{3} - 61606 a^{2} + 39495 a + 56982\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-391a^{4}+521a^{3}+2086a^{2}-1593a-2550\right){x}+12311a^{4}-14868a^{3}-61606a^{2}+39495a+56982$ |
| 9.2-d1 |
9.2-d |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{3} \) |
$47.36641$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.071816150$ |
$1391.221685$ |
2.34806870 |
\( -2645283862896 a^{4} - 1046457240939 a^{3} + 8074249642902 a^{2} + 825633211055 a - 3312687282240 \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 5 a^{2} + a + 5\) , \( a^{2} - 1\) , \( 4 a^{4} - 17 a^{3} + 12 a^{2} + 12 a - 4\) , \( -a^{3} + 3 a + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+a+5\right){x}^{2}+\left(4a^{4}-17a^{3}+12a^{2}+12a-4\right){x}-a^{3}+3a+1$ |
| 9.2-d2 |
9.2-d |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$47.36641$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.023938716$ |
$4173.665056$ |
2.34806870 |
\( 255477 a^{4} - 141634 a^{3} - 1230474 a^{2} + 11085 a + 530487 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{2} - a - 2\) , \( -2 a^{4} - a^{3} + 6 a^{2} - a - 1\) , \( 4 a^{4} + 2 a^{3} - 12 a^{2} - 2 a + 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-4\right){x}^{2}+\left(-2a^{4}-a^{3}+6a^{2}-a-1\right){x}+4a^{4}+2a^{3}-12a^{2}-2a+4$ |
| 9.2-e1 |
9.2-e |
$1$ |
$1$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{6} \) |
$47.36641$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$506.5262400$ |
2.38080751 |
\( -190177 a^{4} - 60439 a^{3} + 567776 a^{2} + 46101 a - 237069 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 5\) , \( -a^{3} + 4 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -13 a^{4} - 3 a^{3} + 70 a^{2} + 42 a - 32\) , \( 194 a^{4} - 127 a^{3} - 911 a^{2} + 90 a + 367\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+5\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-13a^{4}-3a^{3}+70a^{2}+42a-32\right){x}+194a^{4}-127a^{3}-911a^{2}+90a+367$ |
| 9.2-f1 |
9.2-f |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{9} \) |
$47.36641$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.052381833$ |
$2935.427691$ |
3.61363613 |
\( -2645283862896 a^{4} - 1046457240939 a^{3} + 8074249642902 a^{2} + 825633211055 a - 3312687282240 \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 3\) , \( a^{4} - 6 a^{2} - 2 a + 6\) , \( a^{4} - 5 a^{2} - 2 a + 4\) , \( -7 a^{4} - 2 a^{3} + 19 a^{2} - 2 a - 3\) , \( 24 a^{4} + 17 a^{3} - 62 a^{2} - 13 a + 27\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+3\right){x}{y}+\left(a^{4}-5a^{2}-2a+4\right){y}={x}^{3}+\left(a^{4}-6a^{2}-2a+6\right){x}^{2}+\left(-7a^{4}-2a^{3}+19a^{2}-2a-3\right){x}+24a^{4}+17a^{3}-62a^{2}-13a+27$ |
| 9.2-f2 |
9.2-f |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{3} \) |
$47.36641$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 2 \) |
$0.017460611$ |
$8806.283073$ |
3.61363613 |
\( 255477 a^{4} - 141634 a^{3} - 1230474 a^{2} + 11085 a + 530487 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -3 a^{4} + 7 a^{3} + 2 a^{2} - 5 a + 2\) , \( -5 a^{4} + 22 a^{3} - 21 a^{2} - 13 a + 12\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}-2a+2\right){x}^{2}+\left(-3a^{4}+7a^{3}+2a^{2}-5a+2\right){x}-5a^{4}+22a^{3}-21a^{2}-13a+12$ |
| 9.2-g1 |
9.2-g |
$1$ |
$1$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{7} \) |
$47.36641$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$746.3235706$ |
3.50791849 |
\( \frac{3993811}{3} a^{4} - \frac{2195006}{3} a^{3} - \frac{19267171}{3} a^{2} + \frac{441772}{3} a + \frac{8156348}{3} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 4\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 5\) , \( 3 a^{3} + 7 a^{2} - 2 a - 7\) , \( -10 a^{4} - 2 a^{3} + 36 a^{2} + 3 a - 20\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+4\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+5\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-a-1\right){x}^{2}+\left(3a^{3}+7a^{2}-2a-7\right){x}-10a^{4}-2a^{3}+36a^{2}+3a-20$ |
| 9.2-h1 |
9.2-h |
$1$ |
$1$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{9} \) |
$47.36641$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.455375295$ |
$308.5861868$ |
3.30246549 |
\( 59073422 a^{4} - 83449337 a^{3} - 279091818 a^{2} + 236795571 a + 236106333 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 5\) , \( a^{3} - 4 a - 1\) , \( 5 a^{4} - 7 a^{3} - 22 a^{2} + 19 a + 14\) , \( 2 a^{4} - 4 a^{3} - 6 a^{2} + 11 a - 4\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+5\right){x}^{2}+\left(5a^{4}-7a^{3}-22a^{2}+19a+14\right){x}+2a^{4}-4a^{3}-6a^{2}+11a-4$ |
| 9.3-a1 |
9.3-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{10} \) |
$47.36641$ |
$(a^4-a^3-5a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$530.5144716$ |
2.49355855 |
\( \frac{836279}{81} a^{4} - \frac{830812}{27} a^{3} - \frac{1182530}{81} a^{2} + \frac{7789456}{81} a - \frac{1678871}{27} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a + 4\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 3 a^{4} - 5 a^{3} - 10 a^{2} + 8 a + 9\) , \( a^{4} - a^{3} - 6 a^{2} + 4 a + 4\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+4a+4\right){x}^{2}+\left(3a^{4}-5a^{3}-10a^{2}+8a+9\right){x}+a^{4}-a^{3}-6a^{2}+4a+4$ |
| 9.3-a2 |
9.3-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{18} \) |
$47.36641$ |
$(a^4-a^3-5a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$530.5144716$ |
2.49355855 |
\( -\frac{33190771}{531441} a^{4} - \frac{40457941}{177147} a^{3} - \frac{149140862}{531441} a^{2} + \frac{390143776}{531441} a + \frac{255680749}{177147} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + a + 4\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{4} - 3 a^{3} + 4 a^{2} + 5 a + 2\) , \( -2 a^{4} - 3 a^{3} + 3 a^{2} + 5 a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+a+4\right){x}^{2}+\left(-a^{4}-3a^{3}+4a^{2}+5a+2\right){x}-2a^{4}-3a^{3}+3a^{2}+5a+1$ |
| 9.3-b1 |
9.3-b |
$1$ |
$1$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
9.3 |
\( 3^{2} \) |
\( - 3^{6} \) |
$47.36641$ |
$(a^4-a^3-5a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$306.2129818$ |
1.43928213 |
\( -190177 a^{4} - 60439 a^{3} + 567776 a^{2} + 46101 a - 237069 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -2 a^{4} + 7 a^{3} - 3 a^{2} - 8 a + 4\) , \( -4 a^{4} + 16 a^{3} - 13 a^{2} - 10 a + 8\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+3\right){x}^{2}+\left(-2a^{4}+7a^{3}-3a^{2}-8a+4\right){x}-4a^{4}+16a^{3}-13a^{2}-10a+8$ |
| 25.1-a1 |
25.1-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{2} \) |
$52.46144$ |
$(a^3-2a^2-3a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.014349913$ |
$21629.26971$ |
3.64714875 |
\( -\frac{48803087}{5} a^{4} + \frac{185083624}{5} a^{3} - 27082805 a^{2} - \frac{101317246}{5} a + \frac{82622024}{5} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{2} - a - 1\) , \( -5 a^{4} + 3 a^{3} + 30 a^{2} - 7 a - 24\) , \( -a^{4} + a^{3} + 4 a^{2} - a + 7\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(-5a^{4}+3a^{3}+30a^{2}-7a-24\right){x}-a^{4}+a^{3}+4a^{2}-a+7$ |
| 25.1-a2 |
25.1-a |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{6} \) |
$52.46144$ |
$(a^3-2a^2-3a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.043049739$ |
$7209.756571$ |
3.64714875 |
\( \frac{28069349767}{125} a^{4} - \frac{37403782797}{125} a^{3} - \frac{137248787392}{125} a^{2} + \frac{104873423319}{125} a + \frac{5046062774}{5} \) |
\( \bigl[a^{3} - 3 a - 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a\) , \( a^{4} - 5 a^{2} - 2 a + 4\) , \( -9 a^{4} - 3 a^{3} + 57 a^{2} + 32 a - 43\) , \( -50 a^{4} - 2 a^{3} + 282 a^{2} + 118 a - 194\bigr] \) |
${y}^2+\left(a^{3}-3a-1\right){x}{y}+\left(a^{4}-5a^{2}-2a+4\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-4a\right){x}^{2}+\left(-9a^{4}-3a^{3}+57a^{2}+32a-43\right){x}-50a^{4}-2a^{3}+282a^{2}+118a-194$ |
| 25.1-b1 |
25.1-b |
$1$ |
$1$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{2} \) |
$52.46144$ |
$(a^3-2a^2-3a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.010220239$ |
$14216.10920$ |
1.70727776 |
\( 7735 a^{4} - \frac{34594}{5} a^{3} - \frac{244456}{5} a^{2} + \frac{150814}{5} a + \frac{230852}{5} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 5\) , \( 3 a^{4} - 4 a^{3} - 15 a^{2} + 11 a + 15\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+5\right){x}^{2}+\left(3a^{4}-4a^{3}-15a^{2}+11a+15\right){x}$ |
| 27.2-a1 |
27.2-a |
$4$ |
$6$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{24} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \cdot 5 \) |
$1$ |
$119.4376869$ |
2.10520788 |
\( -\frac{1416545484647827595}{14348907} a^{4} + \frac{260450512954909675}{4782969} a^{3} + \frac{6797899957978733561}{14348907} a^{2} - \frac{69668946758877691}{14348907} a - \frac{977999995651724416}{4782969} \) |
\( \bigl[a^{4} - 6 a^{2} + 6\) , \( -a^{4} + 5 a^{2} + a - 3\) , \( a^{4} - 6 a^{2} + 6\) , \( -47 a^{4} + 57 a^{3} + 225 a^{2} - 156 a - 204\) , \( -338 a^{4} + 436 a^{3} + 1639 a^{2} - 1227 a - 1493\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}+6\right){x}{y}+\left(a^{4}-6a^{2}+6\right){y}={x}^{3}+\left(-a^{4}+5a^{2}+a-3\right){x}^{2}+\left(-47a^{4}+57a^{3}+225a^{2}-156a-204\right){x}-338a^{4}+436a^{3}+1639a^{2}-1227a-1493$ |
| 27.2-a2 |
27.2-a |
$4$ |
$6$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{8} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$358.3130608$ |
2.10520788 |
\( -\frac{70262882792}{243} a^{4} - \frac{9259286045}{81} a^{3} + \frac{214460809526}{243} a^{2} + \frac{21878621144}{243} a - \frac{29319663922}{81} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 5\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 5 a + 5\) , \( 1\) , \( 22 a^{4} - 20 a^{3} - 103 a^{2} + 36 a + 53\) , \( 55 a^{4} - 40 a^{3} - 260 a^{2} + 46 a + 120\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+5\right){x}{y}+{y}={x}^{3}+\left(a^{4}-2a^{3}-5a^{2}+5a+5\right){x}^{2}+\left(22a^{4}-20a^{3}-103a^{2}+36a+53\right){x}+55a^{4}-40a^{3}-260a^{2}+46a+120$ |
| 27.2-a3 |
27.2-a |
$4$ |
$6$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{39} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \cdot 5 \) |
$1$ |
$59.71884347$ |
2.10520788 |
\( \frac{30895452362328521001610}{205891132094649} a^{4} - \frac{38485846124257344963563}{68630377364883} a^{3} + \frac{80820513113928805539305}{205891132094649} a^{2} + \frac{64618298845123337694905}{205891132094649} a - \frac{16048051024068932702644}{68630377364883} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( 1\) , \( -127 a^{4} + 508 a^{3} - 412 a^{2} - 287 a + 242\) , \( 3257 a^{4} - 12293 a^{3} + 8914 a^{2} + 6660 a - 5416\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+{y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2\right){x}^{2}+\left(-127a^{4}+508a^{3}-412a^{2}-287a+242\right){x}+3257a^{4}-12293a^{3}+8914a^{2}+6660a-5416$ |
| 27.2-a4 |
27.2-a |
$4$ |
$6$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{13} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 5 \) |
$1$ |
$179.1565304$ |
2.10520788 |
\( \frac{105438354859995395583607}{59049} a^{4} + \frac{13903576042602911901544}{19683} a^{3} - \frac{321831470140232973704590}{59049} a^{2} - \frac{32908894842329964654919}{59049} a + \frac{44013458350534380713159}{19683} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - 5 a\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -15 a^{4} + 37 a^{3} + 25 a^{2} - 52 a - 30\) , \( 31 a^{4} - 78 a^{3} - 43 a^{2} + 106 a + 48\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-15a^{4}+37a^{3}+25a^{2}-52a-30\right){x}+31a^{4}-78a^{3}-43a^{2}+106a+48$ |
| 27.2-b1 |
27.2-b |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{10} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.034839024$ |
$1412.146267$ |
4.62485365 |
\( \frac{836279}{81} a^{4} - \frac{830812}{27} a^{3} - \frac{1182530}{81} a^{2} + \frac{7789456}{81} a - \frac{1678871}{27} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 5\) , \( a^{4} - 5 a^{2} - a + 3\) , \( 6 a^{4} - 9 a^{3} - 23 a^{2} + 24 a + 6\) , \( 3 a^{4} - 11 a^{3} - 6 a^{2} + 35 a - 12\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{4}-5a^{2}-a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+3a+5\right){x}^{2}+\left(6a^{4}-9a^{3}-23a^{2}+24a+6\right){x}+3a^{4}-11a^{3}-6a^{2}+35a-12$ |
| 27.2-b2 |
27.2-b |
$2$ |
$3$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{18} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.011613008$ |
$1412.146267$ |
4.62485365 |
\( -\frac{33190771}{531441} a^{4} - \frac{40457941}{177147} a^{3} - \frac{149140862}{531441} a^{2} + \frac{390143776}{531441} a + \frac{255680749}{177147} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a\) , \( a^{2} - a - 2\) , \( 37 a^{4} - 50 a^{3} - 178 a^{2} + 138 a + 168\) , \( 14 a^{4} - 18 a^{3} - 65 a^{2} + 47 a + 55\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+3a\right){x}^{2}+\left(37a^{4}-50a^{3}-178a^{2}+138a+168\right){x}+14a^{4}-18a^{3}-65a^{2}+47a+55$ |
| 27.2-c1 |
27.2-c |
$4$ |
$4$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{37} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$28.75563817$ |
1.08127294 |
\( \frac{23528616372387310155348371}{22876792454961} a^{4} - \frac{89094465321390947073627637}{22876792454961} a^{3} + \frac{65065606781630428155559141}{22876792454961} a^{2} + \frac{48451040387946407286293738}{22876792454961} a - \frac{39507407995806247013574710}{22876792454961} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 4\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -124 a^{4} - 49 a^{3} + 358 a^{2} + 34 a - 143\) , \( 753 a^{4} + 217 a^{3} - 2492 a^{2} - 203 a + 1032\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+4\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-124a^{4}-49a^{3}+358a^{2}+34a-143\right){x}+753a^{4}+217a^{3}-2492a^{2}-203a+1032$ |
| 27.2-c2 |
27.2-c |
$4$ |
$4$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{26} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$230.0451054$ |
1.08127294 |
\( \frac{289876034537}{4782969} a^{4} - \frac{2000730083710}{4782969} a^{3} + \frac{3814114508431}{4782969} a^{2} - \frac{1391444238889}{4782969} a - \frac{220812972785}{4782969} \) |
\( \bigl[a^{4} - 6 a^{2} - a + 5\) , \( -a^{2} + 2\) , \( a^{2} - 1\) , \( -36 a^{4} + 54 a^{3} + 153 a^{2} - 124 a - 137\) , \( 47 a^{4} - 35 a^{3} - 319 a^{2} + 198 a + 283\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-a+5\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-36a^{4}+54a^{3}+153a^{2}-124a-137\right){x}+47a^{4}-35a^{3}-319a^{2}+198a+283$ |
| 27.2-c3 |
27.2-c |
$4$ |
$4$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( 3^{16} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1840.360843$ |
1.08127294 |
\( -\frac{407561}{2187} a^{4} + \frac{37105}{2187} a^{3} + \frac{2315240}{2187} a^{2} - \frac{1082642}{2187} a + \frac{2216858}{2187} \) |
\( \bigl[a^{4} - 6 a^{2} - a + 5\) , \( -a^{2} + 2\) , \( a^{2} - 1\) , \( 4 a^{4} - 6 a^{3} - 22 a^{2} + 21 a + 28\) , \( 13 a^{4} - 18 a^{3} - 66 a^{2} + 53 a + 64\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-a+5\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(4a^{4}-6a^{3}-22a^{2}+21a+28\right){x}+13a^{4}-18a^{3}-66a^{2}+53a+64$ |
| 27.2-c4 |
27.2-c |
$4$ |
$4$ |
5.5.181057.1 |
$5$ |
$[5, 0]$ |
27.2 |
\( 3^{3} \) |
\( - 3^{25} \) |
$52.86675$ |
$(a), (a^4-a^3-5a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$7.188909544$ |
1.08127294 |
\( -\frac{34495656525909971}{531441} a^{4} + \frac{28517667503038951}{177147} a^{3} + \frac{81066375780822875}{531441} a^{2} - \frac{258890063675704426}{531441} a + \frac{39365969687406722}{177147} \) |
\( \bigl[a^{4} - 6 a^{2} - a + 5\) , \( -a^{2} + 2\) , \( a^{2} - 1\) , \( -221 a^{4} + 299 a^{3} + 1068 a^{2} - 819 a - 1007\) , \( -2885 a^{4} + 3879 a^{3} + 14030 a^{2} - 10778 a - 13016\bigr] \) |
${y}^2+\left(a^{4}-6a^{2}-a+5\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-221a^{4}+299a^{3}+1068a^{2}-819a-1007\right){x}-2885a^{4}+3879a^{3}+14030a^{2}-10778a-13016$ |
*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.
