| 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 |
| 3.1-a1 |
3.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{12} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$9.481677475$ |
1.87051772 |
\( -\frac{168597349538283793255196523870168742}{531441} a^{4} - \frac{146951452671406161470630956150286186}{531441} a^{3} + \frac{883499465404971970945729761296163359}{531441} a^{2} + \frac{938665978916056043935046842568594930}{531441} a - \frac{193431679337629280885460277104936977}{531441} \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 4 a + 3\) , \( 12 a^{4} + 22 a^{3} - 72 a^{2} + 61 a - 21\) , \( 1072 a^{4} + 2972 a^{3} - 864 a^{2} - 2777 a + 490\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-a^{2}-4a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a-1\right){x}^{2}+\left(12a^{4}+22a^{3}-72a^{2}+61a-21\right){x}+1072a^{4}+2972a^{3}-864a^{2}-2777a+490$ |
| 3.1-a2 |
3.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$28.44503242$ |
1.87051772 |
\( \frac{693610586914425506}{81} a^{4} - \frac{1341521205063857732}{81} a^{3} - \frac{1566992156341261273}{81} a^{2} + \frac{2337096975295311995}{81} a - \frac{358591099563782834}{81} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 2\) , \( -67 a^{4} + 108 a^{3} + 187 a^{2} - 165 a - 33\) , \( -622 a^{4} + 1127 a^{3} + 1534 a^{2} - 1907 a + 104\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-5a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a+1\right){x}^{2}+\left(-67a^{4}+108a^{3}+187a^{2}-165a-33\right){x}-622a^{4}+1127a^{3}+1534a^{2}-1907a+104$ |
| 3.1-a3 |
3.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{24} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
|
\( 2 \) |
$1$ |
$303.4136792$ |
1.87051772 |
\( -\frac{62241338070079101267117803}{282429536481} a^{4} - \frac{54250289643689607508842292}{282429536481} a^{3} + \frac{326162831513667259536223918}{282429536481} a^{2} + \frac{346528736595990608471673124}{282429536481} a - \frac{71409465093774942174954271}{282429536481} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( -a^{4} + 6 a^{2} + a - 3\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( 174 a^{4} - 252 a^{3} - 688 a^{2} + 838 a - 141\) , \( 354 a^{4} - 503 a^{3} - 1411 a^{2} + 1660 a - 247\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-3\right){x}^{2}+\left(174a^{4}-252a^{3}-688a^{2}+838a-141\right){x}+354a^{4}-503a^{3}-1411a^{2}+1660a-247$ |
| 3.1-a4 |
3.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
|
\( 2 \) |
$1$ |
$910.2410376$ |
1.87051772 |
\( \frac{58014767521}{6561} a^{4} - \frac{167697632446}{6561} a^{3} + \frac{57803977501}{6561} a^{2} + \frac{45994881784}{6561} a - \frac{5697274756}{6561} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( a^{4} + a^{3} - 7 a^{2} - 6 a + 5\) , \( a^{4} - 4 a^{2} - 2 a + 1\) , \( 50 a^{4} + 41 a^{3} - 263 a^{2} - 268 a + 66\) , \( 276 a^{4} + 243 a^{3} - 1446 a^{2} - 1548 a + 307\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){x}{y}+\left(a^{4}-4a^{2}-2a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-6a+5\right){x}^{2}+\left(50a^{4}+41a^{3}-263a^{2}-268a+66\right){x}+276a^{4}+243a^{3}-1446a^{2}-1548a+307$ |
| 3.1-a5 |
3.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$1820.482075$ |
1.87051772 |
\( \frac{7255}{81} a^{4} + \frac{52427}{81} a^{3} - \frac{198911}{81} a^{2} + \frac{176566}{81} a - \frac{42403}{81} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( a^{4} + a^{3} - 7 a^{2} - 6 a + 5\) , \( a^{4} - 4 a^{2} - 2 a + 1\) , \( 5 a^{4} + a^{3} - 28 a^{2} - 13 a + 21\) , \( 14 a^{4} + 11 a^{3} - 77 a^{2} - 71 a + 30\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){x}{y}+\left(a^{4}-4a^{2}-2a+1\right){y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-6a+5\right){x}^{2}+\left(5a^{4}+a^{3}-28a^{2}-13a+21\right){x}+14a^{4}+11a^{3}-77a^{2}-71a+30$ |
| 3.1-a6 |
3.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$606.8273584$ |
1.87051772 |
\( \frac{15943602679948}{531441} a^{4} + \frac{32563697530457}{531441} a^{3} - \frac{23905736489783}{531441} a^{2} - \frac{48004702564172}{531441} a + \frac{9074974737938}{531441} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( -a^{4} + 6 a^{2} + a - 3\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( -46 a^{4} + 63 a^{3} + 187 a^{2} - 207 a + 24\) , \( -45 a^{4} + 63 a^{3} + 181 a^{2} - 208 a + 28\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-3\right){x}^{2}+\left(-46a^{4}+63a^{3}+187a^{2}-207a+24\right){x}-45a^{4}+63a^{3}+181a^{2}-208a+28$ |
| 3.1-a7 |
3.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{48} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$151.7068396$ |
1.87051772 |
\( \frac{566559582687648619287860470150}{79766443076872509863361} a^{4} - \frac{218887186908007195176218076790}{79766443076872509863361} a^{3} - \frac{3720425094387933252600411583823}{79766443076872509863361} a^{2} + \frac{445981655523035563751693511022}{79766443076872509863361} a + \frac{5282169287046497532534894177713}{79766443076872509863361} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 4\) , \( a^{4} - 4 a^{2} - 2 a\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 12 a^{4} - 6 a^{3} - 136 a^{2} - 190 a - 68\) , \( 234 a^{4} - 83 a^{3} - 2050 a^{2} - 1595 a + 708\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+4\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){y}={x}^{3}+\left(a^{4}-4a^{2}-2a\right){x}^{2}+\left(12a^{4}-6a^{3}-136a^{2}-190a-68\right){x}+234a^{4}-83a^{3}-2050a^{2}-1595a+708$ |
| 3.1-a8 |
3.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
|
\( 2 \) |
$1$ |
$455.1205188$ |
1.87051772 |
\( -\frac{90869581629544410130562}{43046721} a^{4} + \frac{130714114751761584656900}{43046721} a^{3} + \frac{357187878123487095538249}{43046721} a^{2} - \frac{422938115961114864282827}{43046721} a + \frac{63170554841433736251746}{43046721} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a + 1\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 2\) , \( 63 a^{4} - 102 a^{3} - 263 a^{2} + 325 a - 53\) , \( -494 a^{4} + 641 a^{3} + 1864 a^{2} - 2153 a + 318\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-5a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a+1\right){x}^{2}+\left(63a^{4}-102a^{3}-263a^{2}+325a-53\right){x}-494a^{4}+641a^{3}+1864a^{2}-2153a+318$ |
| 3.1-b1 |
3.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{12} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.459393568$ |
$619.6859337$ |
1.87413286 |
\( -\frac{168597349538283793255196523870168742}{531441} a^{4} - \frac{146951452671406161470630956150286186}{531441} a^{3} + \frac{883499465404971970945729761296163359}{531441} a^{2} + \frac{938665978916056043935046842568594930}{531441} a - \frac{193431679337629280885460277104936977}{531441} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 5 a\) , \( a^{3} - 4 a\) , \( -854 a^{4} + 1664 a^{3} + 1896 a^{2} - 2860 a + 435\) , \( 34141 a^{4} - 66047 a^{3} - 77002 a^{2} + 114944 a - 17637\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-854a^{4}+1664a^{3}+1896a^{2}-2860a+435\right){x}+34141a^{4}-66047a^{3}-77002a^{2}+114944a-17637$ |
| 3.1-b2 |
3.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.153131189$ |
$1859.057801$ |
1.87413286 |
\( \frac{693610586914425506}{81} a^{4} - \frac{1341521205063857732}{81} a^{3} - \frac{1566992156341261273}{81} a^{2} + \frac{2337096975295311995}{81} a - \frac{358591099563782834}{81} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( -a^{4} - a^{3} + 6 a^{2} + 5 a - 3\) , \( a^{3} - 4 a\) , \( -32 a^{4} - 18 a^{3} + 192 a^{2} + 113 a - 206\) , \( 118 a^{4} - 282 a^{3} - 1247 a^{2} + 25 a + 1049\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+5a-3\right){x}^{2}+\left(-32a^{4}-18a^{3}+192a^{2}+113a-206\right){x}+118a^{4}-282a^{3}-1247a^{2}+25a+1049$ |
| 3.1-b3 |
3.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{24} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.918787136$ |
$1239.371867$ |
1.87413286 |
\( -\frac{62241338070079101267117803}{282429536481} a^{4} - \frac{54250289643689607508842292}{282429536481} a^{3} + \frac{326162831513667259536223918}{282429536481} a^{2} + \frac{346528736595990608471673124}{282429536481} a - \frac{71409465093774942174954271}{282429536481} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 5 a\) , \( a^{3} - 4 a\) , \( -74 a^{4} + 139 a^{3} + 166 a^{2} - 240 a + 35\) , \( 53 a^{4} - 97 a^{3} - 123 a^{2} + 174 a - 27\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-74a^{4}+139a^{3}+166a^{2}-240a+35\right){x}+53a^{4}-97a^{3}-123a^{2}+174a-27$ |
| 3.1-b4 |
3.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2 \) |
$0.306262378$ |
$3718.115602$ |
1.87413286 |
\( \frac{58014767521}{6561} a^{4} - \frac{167697632446}{6561} a^{3} + \frac{57803977501}{6561} a^{2} + \frac{45994881784}{6561} a - \frac{5697274756}{6561} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 3\) , \( -a^{4} + 6 a^{2} + 2 a - 5\) , \( a^{3} - 3 a + 1\) , \( 347 a^{4} + 306 a^{3} - 1822 a^{2} - 1943 a + 400\) , \( -6146 a^{4} - 5363 a^{3} + 32211 a^{2} + 34237 a - 7052\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+3\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+2a-5\right){x}^{2}+\left(347a^{4}+306a^{3}-1822a^{2}-1943a+400\right){x}-6146a^{4}-5363a^{3}+32211a^{2}+34237a-7052$ |
| 3.1-b5 |
3.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.153131189$ |
$7436.231205$ |
1.87413286 |
\( \frac{7255}{81} a^{4} + \frac{52427}{81} a^{3} - \frac{198911}{81} a^{2} + \frac{176566}{81} a - \frac{42403}{81} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 3\) , \( -a^{4} + 6 a^{2} + 2 a - 5\) , \( a^{3} - 3 a + 1\) , \( 7 a^{4} + 6 a^{3} - 37 a^{2} - 38 a + 10\) , \( -231 a^{4} - 202 a^{3} + 1210 a^{2} + 1287 a - 266\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+3\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+2a-5\right){x}^{2}+\left(7a^{4}+6a^{3}-37a^{2}-38a+10\right){x}-231a^{4}-202a^{3}+1210a^{2}+1287a-266$ |
| 3.1-b6 |
3.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.459393568$ |
$2478.743735$ |
1.87413286 |
\( \frac{15943602679948}{531441} a^{4} + \frac{32563697530457}{531441} a^{3} - \frac{23905736489783}{531441} a^{2} - \frac{48004702564172}{531441} a + \frac{9074974737938}{531441} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 5 a\) , \( a^{3} - 4 a\) , \( 16 a^{4} - 36 a^{3} - 34 a^{2} + 60 a - 10\) , \( 36 a^{4} - 65 a^{3} - 80 a^{2} + 111 a - 17\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(16a^{4}-36a^{3}-34a^{2}+60a-10\right){x}+36a^{4}-65a^{3}-80a^{2}+111a-17$ |
| 3.1-b7 |
3.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{48} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$1.837574272$ |
$38.73037086$ |
1.87413286 |
\( \frac{566559582687648619287860470150}{79766443076872509863361} a^{4} - \frac{218887186908007195176218076790}{79766443076872509863361} a^{3} - \frac{3720425094387933252600411583823}{79766443076872509863361} a^{2} + \frac{445981655523035563751693511022}{79766443076872509863361} a + \frac{5282169287046497532534894177713}{79766443076872509863361} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 5 a + 3\) , \( a^{4} - 4 a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 349 a^{4} + 334 a^{3} - 1852 a^{2} - 2045 a + 385\) , \( -7186 a^{4} - 6100 a^{3} + 37489 a^{2} + 39457 a - 8208\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-5a+3\right){x}{y}+\left(a^{3}-a^{2}-4a+2\right){y}={x}^{3}+\left(a^{4}-4a^{2}-3a-1\right){x}^{2}+\left(349a^{4}+334a^{3}-1852a^{2}-2045a+385\right){x}-7186a^{4}-6100a^{3}+37489a^{2}+39457a-8208$ |
| 3.1-b8 |
3.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$37.87450$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2 \) |
$0.612524757$ |
$116.1911125$ |
1.87413286 |
\( -\frac{90869581629544410130562}{43046721} a^{4} + \frac{130714114751761584656900}{43046721} a^{3} + \frac{357187878123487095538249}{43046721} a^{2} - \frac{422938115961114864282827}{43046721} a + \frac{63170554841433736251746}{43046721} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 4\) , \( -a^{2} - a + 2\) , \( 1\) , \( -61 a^{4} + 136 a^{3} + 74 a^{2} - 151 a + 26\) , \( 1511 a^{4} - 2792 a^{3} - 3854 a^{2} + 5430 a - 828\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(-61a^{4}+136a^{3}+74a^{2}-151a+26\right){x}+1511a^{4}-2792a^{3}-3854a^{2}+5430a-828$ |
| 9.1-a1 |
9.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{18} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$144$ |
\( 2 \) |
$1$ |
$9.554420731$ |
1.81150975 |
\( -\frac{168597349538283793255196523870168742}{531441} a^{4} - \frac{146951452671406161470630956150286186}{531441} a^{3} + \frac{883499465404971970945729761296163359}{531441} a^{2} + \frac{938665978916056043935046842568594930}{531441} a - \frac{193431679337629280885460277104936977}{531441} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 3\) , \( 114 a^{4} + 100 a^{3} - 586 a^{2} - 606 a + 88\) , \( 1310 a^{4} + 911 a^{3} - 7022 a^{2} - 6840 a + 1535\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-a-2\right){x}^{2}+\left(114a^{4}+100a^{3}-586a^{2}-606a+88\right){x}+1310a^{4}+911a^{3}-7022a^{2}-6840a+1535$ |
| 9.1-a2 |
9.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$16$ |
\( 2 \) |
$1$ |
$773.9080792$ |
1.81150975 |
\( \frac{693610586914425506}{81} a^{4} - \frac{1341521205063857732}{81} a^{3} - \frac{1566992156341261273}{81} a^{2} + \frac{2337096975295311995}{81} a - \frac{358591099563782834}{81} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 0\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 64 a^{4} + 104 a^{3} - 335 a^{2} - 554 a - 77\) , \( 1654 a^{4} + 1213 a^{3} - 8700 a^{2} - 8238 a + 2686\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){y}={x}^{3}+\left(64a^{4}+104a^{3}-335a^{2}-554a-77\right){x}+1654a^{4}+1213a^{3}-8700a^{2}-8238a+2686$ |
| 9.1-a3 |
9.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{30} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.2 |
$36$ |
\( 2^{2} \) |
$1$ |
$76.43536584$ |
1.81150975 |
\( -\frac{62241338070079101267117803}{282429536481} a^{4} - \frac{54250289643689607508842292}{282429536481} a^{3} + \frac{326162831513667259536223918}{282429536481} a^{2} + \frac{346528736595990608471673124}{282429536481} a - \frac{71409465093774942174954271}{282429536481} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 3\) , \( 4 a^{4} - 31 a^{2} - 31 a - 2\) , \( -8 a^{4} - 56 a^{3} - 106 a^{2} - 51 a + 7\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-a-2\right){x}^{2}+\left(4a^{4}-31a^{2}-31a-2\right){x}-8a^{4}-56a^{3}-106a^{2}-51a+7$ |
| 9.1-a4 |
9.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$6191.264633$ |
1.81150975 |
\( \frac{58014767521}{6561} a^{4} - \frac{167697632446}{6561} a^{3} + \frac{57803977501}{6561} a^{2} + \frac{45994881784}{6561} a - \frac{5697274756}{6561} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 0\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 4 a^{4} + 4 a^{3} - 20 a^{2} - 24 a - 7\) , \( 37 a^{4} + 31 a^{3} - 196 a^{2} - 201 a + 56\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){y}={x}^{3}+\left(4a^{4}+4a^{3}-20a^{2}-24a-7\right){x}+37a^{4}+31a^{3}-196a^{2}-201a+56$ |
| 9.1-a5 |
9.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$6191.264633$ |
1.81150975 |
\( \frac{7255}{81} a^{4} + \frac{52427}{81} a^{3} - \frac{198911}{81} a^{2} + \frac{176566}{81} a - \frac{42403}{81} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 0\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 6 a - 2\) , \( -a^{4} - a^{3} + 5 a^{2} + 6 a - 1\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+6a-2\right){x}-a^{4}-a^{3}+5a^{2}+6a-1$ |
| 9.1-a6 |
9.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$76.43536584$ |
1.81150975 |
\( \frac{15943602679948}{531441} a^{4} + \frac{32563697530457}{531441} a^{3} - \frac{23905736489783}{531441} a^{2} - \frac{48004702564172}{531441} a + \frac{9074974737938}{531441} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 4\) , \( -9 a^{4} + 17 a^{3} + 34 a^{2} - 60 a + 10\) , \( -6 a^{4} + 10 a^{3} + 24 a^{2} - 34 a + 2\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+4\right){y}={x}^{3}+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}^{2}+\left(-9a^{4}+17a^{3}+34a^{2}-60a+10\right){x}-6a^{4}+10a^{3}+24a^{2}-34a+2$ |
| 9.1-a7 |
9.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{54} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$36$ |
\( 2^{2} \) |
$1$ |
$19.10884146$ |
1.81150975 |
\( \frac{566559582687648619287860470150}{79766443076872509863361} a^{4} - \frac{218887186908007195176218076790}{79766443076872509863361} a^{3} - \frac{3720425094387933252600411583823}{79766443076872509863361} a^{2} + \frac{445981655523035563751693511022}{79766443076872509863361} a + \frac{5282169287046497532534894177713}{79766443076872509863361} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{4} + a^{3} + 5 a^{2} - a - 2\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 3\) , \( -26 a^{4} - 20 a^{3} + 124 a^{2} + 64 a - 172\) , \( -130 a^{4} + 49 a^{3} + 742 a^{2} + 14 a - 693\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-a-2\right){x}^{2}+\left(-26a^{4}-20a^{3}+124a^{2}+64a-172\right){x}-130a^{4}+49a^{3}+742a^{2}+14a-693$ |
| 9.1-a8 |
9.1-a |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{22} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$1547.816158$ |
1.81150975 |
\( -\frac{90869581629544410130562}{43046721} a^{4} + \frac{130714114751761584656900}{43046721} a^{3} + \frac{357187878123487095538249}{43046721} a^{2} - \frac{422938115961114864282827}{43046721} a + \frac{63170554841433736251746}{43046721} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 0\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( 24 a^{4} - 16 a^{3} - 105 a^{2} + 26 a - 17\) , \( -48 a^{4} + 117 a^{3} + 164 a^{2} - 432 a + 74\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){y}={x}^{3}+\left(24a^{4}-16a^{3}-105a^{2}+26a-17\right){x}-48a^{4}+117a^{3}+164a^{2}-432a+74$ |
| 9.1-b1 |
9.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{18} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \) |
$1$ |
$74.02382031$ |
1.55942790 |
\( -\frac{168597349538283793255196523870168742}{531441} a^{4} - \frac{146951452671406161470630956150286186}{531441} a^{3} + \frac{883499465404971970945729761296163359}{531441} a^{2} + \frac{938665978916056043935046842568594930}{531441} a - \frac{193431679337629280885460277104936977}{531441} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a\) , \( 125 a^{4} + 347 a^{3} - 597 a^{2} - 1068 a + 206\) , \( -31102 a^{4} - 67393 a^{3} + 26937 a^{2} + 75940 a - 13926\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+3\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-4a+3\right){x}^{2}+\left(125a^{4}+347a^{3}-597a^{2}-1068a+206\right){x}-31102a^{4}-67393a^{3}+26937a^{2}+75940a-13926$ |
| 9.1-b2 |
9.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$16$ |
\( 2 \) |
$1$ |
$74.02382031$ |
1.55942790 |
\( \frac{693610586914425506}{81} a^{4} - \frac{1341521205063857732}{81} a^{3} - \frac{1566992156341261273}{81} a^{2} + \frac{2337096975295311995}{81} a - \frac{358591099563782834}{81} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 2\) , \( a^{4} + a^{3} - 7 a^{2} - 7 a + 6\) , \( 0\) , \( -99 a^{4} - 9 a^{3} + 604 a^{2} + 161 a - 632\) , \( -1347 a^{4} - 279 a^{3} + 8033 a^{2} + 3035 a - 7353\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+2\right){x}{y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-7a+6\right){x}^{2}+\left(-99a^{4}-9a^{3}+604a^{2}+161a-632\right){x}-1347a^{4}-279a^{3}+8033a^{2}+3035a-7353$ |
| 9.1-b3 |
9.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{30} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$592.1905625$ |
1.55942790 |
\( -\frac{62241338070079101267117803}{282429536481} a^{4} - \frac{54250289643689607508842292}{282429536481} a^{3} + \frac{326162831513667259536223918}{282429536481} a^{2} + \frac{346528736595990608471673124}{282429536481} a - \frac{71409465093774942174954271}{282429536481} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{4} - a^{3} + 7 a^{2} + 5 a - 5\) , \( a^{2} - 2\) , \( 43 a^{4} + 64 a^{3} - 255 a^{2} - 323 a + 67\) , \( -349 a^{4} - 208 a^{3} + 1724 a^{2} + 1636 a - 340\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+7a^{2}+5a-5\right){x}^{2}+\left(43a^{4}+64a^{3}-255a^{2}-323a+67\right){x}-349a^{4}-208a^{3}+1724a^{2}+1636a-340$ |
| 9.1-b4 |
9.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$592.1905625$ |
1.55942790 |
\( \frac{58014767521}{6561} a^{4} - \frac{167697632446}{6561} a^{3} + \frac{57803977501}{6561} a^{2} + \frac{45994881784}{6561} a - \frac{5697274756}{6561} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 2\) , \( a^{4} + a^{3} - 7 a^{2} - 7 a + 6\) , \( 0\) , \( -4 a^{4} - 4 a^{3} + 24 a^{2} + 16 a - 32\) , \( -21 a^{4} - 4 a^{3} + 156 a^{2} + 80 a - 164\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+2\right){x}{y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-7a+6\right){x}^{2}+\left(-4a^{4}-4a^{3}+24a^{2}+16a-32\right){x}-21a^{4}-4a^{3}+156a^{2}+80a-164$ |
| 9.1-b5 |
9.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$592.1905625$ |
1.55942790 |
\( \frac{7255}{81} a^{4} + \frac{52427}{81} a^{3} - \frac{198911}{81} a^{2} + \frac{176566}{81} a - \frac{42403}{81} \) |
\( \bigl[a^{4} - 5 a^{2} - 2 a + 2\) , \( a^{4} + a^{3} - 7 a^{2} - 7 a + 6\) , \( 0\) , \( a^{4} + a^{3} - 6 a^{2} - 4 a + 8\) , \( 0\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-2a+2\right){x}{y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-7a+6\right){x}^{2}+\left(a^{4}+a^{3}-6a^{2}-4a+8\right){x}$ |
| 9.1-b6 |
9.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$592.1905625$ |
1.55942790 |
\( \frac{15943602679948}{531441} a^{4} + \frac{32563697530457}{531441} a^{3} - \frac{23905736489783}{531441} a^{2} - \frac{48004702564172}{531441} a + \frac{9074974737938}{531441} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{4} - a^{3} + 7 a^{2} + 5 a - 5\) , \( a^{2} - 2\) , \( 8 a^{4} - 6 a^{3} - 30 a^{2} - 3 a + 7\) , \( 4 a^{4} - 16 a^{3} - a^{2} + 37 a - 9\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+7a^{2}+5a-5\right){x}^{2}+\left(8a^{4}-6a^{3}-30a^{2}-3a+7\right){x}+4a^{4}-16a^{3}-a^{2}+37a-9$ |
| 9.1-b7 |
9.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{54} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$148.0476406$ |
1.55942790 |
\( \frac{566559582687648619287860470150}{79766443076872509863361} a^{4} - \frac{218887186908007195176218076790}{79766443076872509863361} a^{3} - \frac{3720425094387933252600411583823}{79766443076872509863361} a^{2} + \frac{445981655523035563751693511022}{79766443076872509863361} a + \frac{5282169287046497532534894177713}{79766443076872509863361} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{4} - a^{3} + 7 a^{2} + 5 a - 5\) , \( a^{2} - 2\) , \( -67 a^{4} + 259 a^{3} + 20 a^{2} - 638 a + 67\) , \( 1155 a^{4} - 3034 a^{3} - 1828 a^{2} + 6522 a - 897\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}-a^{3}+7a^{2}+5a-5\right){x}^{2}+\left(-67a^{4}+259a^{3}+20a^{2}-638a+67\right){x}+1155a^{4}-3034a^{3}-1828a^{2}+6522a-897$ |
| 9.1-b8 |
9.1-b |
$8$ |
$12$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{22} \) |
$42.27260$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$148.0476406$ |
1.55942790 |
\( -\frac{90869581629544410130562}{43046721} a^{4} + \frac{130714114751761584656900}{43046721} a^{3} + \frac{357187878123487095538249}{43046721} a^{2} - \frac{422938115961114864282827}{43046721} a + \frac{63170554841433736251746}{43046721} \) |
\( \bigl[a^{4} - 4 a^{2} - a\) , \( -a^{4} - a^{3} + 5 a^{2} + 5 a - 1\) , \( a^{4} + a^{3} - 6 a^{2} - 6 a + 5\) , \( -24 a^{4} - 41 a^{3} - 22 a^{2} - 19 a + 3\) , \( 394 a^{4} + 948 a^{3} - 431 a^{2} - 1250 a + 226\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a\right){x}{y}+\left(a^{4}+a^{3}-6a^{2}-6a+5\right){y}={x}^{3}+\left(-a^{4}-a^{3}+5a^{2}+5a-1\right){x}^{2}+\left(-24a^{4}-41a^{3}-22a^{2}-19a+3\right){x}+394a^{4}+948a^{3}-431a^{2}-1250a+226$ |
| 11.1-a1 |
11.1-a |
$4$ |
$15$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{15} \) |
$43.12946$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$1.020931196$ |
$161.5128417$ |
2.17108764 |
\( \frac{1184640118013435456872762923766421719}{4177248169415651} a^{4} - \frac{1704081333239142233648100476267809427}{4177248169415651} a^{3} - \frac{4656553480729461401891695968990292554}{4177248169415651} a^{2} + \frac{5513719783091004539172990813952141067}{4177248169415651} a - \frac{823535932137308495383461031371744326}{4177248169415651} \) |
\( \bigl[a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( a^{4} + a^{3} - 6 a^{2} - 7 a + 3\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( 22 a^{4} + 9 a^{3} - 190 a^{2} - 73 a + 158\) , \( -42 a^{4} - 187 a^{3} + 252 a^{2} + 358 a - 230\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){x}{y}+\left(a^{4}-5a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}+a^{3}-6a^{2}-7a+3\right){x}^{2}+\left(22a^{4}+9a^{3}-190a^{2}-73a+158\right){x}-42a^{4}-187a^{3}+252a^{2}+358a-230$ |
| 11.1-a2 |
11.1-a |
$4$ |
$15$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{5} \) |
$43.12946$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.2 |
$1$ |
\( 1 \) |
$0.340310398$ |
$484.5385253$ |
2.17108764 |
\( \frac{168933940112634861051}{161051} a^{4} - \frac{326043912184238254574}{161051} a^{3} - \frac{381377843583909776903}{161051} a^{2} + \frac{568280423008643207018}{161051} a - \frac{87189080412017164334}{161051} \) |
\( \bigl[1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a - 2\) , \( a^{3} - 4 a + 1\) , \( -391 a^{4} - 141 a^{3} + 2421 a^{2} + 1101 a - 2471\) , \( 10197 a^{4} + 2359 a^{3} - 61559 a^{2} - 23284 a + 59622\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a-2\right){x}^{2}+\left(-391a^{4}-141a^{3}+2421a^{2}+1101a-2471\right){x}+10197a^{4}+2359a^{3}-61559a^{2}-23284a+59622$ |
| 11.1-a3 |
11.1-a |
$4$ |
$15$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$43.12946$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 1 \) |
$0.204186239$ |
$807.5642089$ |
2.17108764 |
\( -\frac{23276749224}{1331} a^{4} + \frac{2036354170}{1331} a^{3} + \frac{162517532725}{1331} a^{2} + \frac{51601850093}{1331} a - \frac{156355149044}{1331} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( -32 a^{4} - 21 a^{3} + 38 a^{2} + 3 a\) , \( 93 a^{4} + 491 a^{3} + 52 a^{2} - 595 a + 100\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-32a^{4}-21a^{3}+38a^{2}+3a\right){x}+93a^{4}+491a^{3}+52a^{2}-595a+100$ |
| 11.1-a4 |
11.1-a |
$4$ |
$15$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$43.12946$ |
$(a^3-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.4.1 |
$1$ |
\( 1 \) |
$0.068062079$ |
$2422.692626$ |
2.17108764 |
\( \frac{117598}{11} a^{4} + \frac{103030}{11} a^{3} - \frac{611217}{11} a^{2} - \frac{661252}{11} a + \frac{135283}{11} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 3\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( 2 a^{4} + 2 a^{3} - 11 a^{2} - 10 a + 9\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+3\right){x}{y}+\left(a^{4}-5a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){x}^{2}+\left(2a^{4}+2a^{3}-11a^{2}-10a+9\right){x}+a^{4}+a^{3}-5a^{2}-5a+2$ |
| 11.1-b1 |
11.1-b |
$4$ |
$15$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{15} \) |
$43.12946$ |
$(a^3-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 3 \cdot 5 \) |
$1$ |
$1.465635829$ |
1.44730865 |
\( \frac{1184640118013435456872762923766421719}{4177248169415651} a^{4} - \frac{1704081333239142233648100476267809427}{4177248169415651} a^{3} - \frac{4656553480729461401891695968990292554}{4177248169415651} a^{2} + \frac{5513719783091004539172990813952141067}{4177248169415651} a - \frac{823535932137308495383461031371744326}{4177248169415651} \) |
\( \bigl[a^{4} - 4 a^{2} - a\) , \( 1\) , \( a^{4} - 4 a^{2} - 2 a + 1\) , \( 1159 a^{4} - 1311 a^{3} - 4998 a^{2} + 3917 a + 552\) , \( 32173 a^{4} - 43110 a^{3} - 130441 a^{2} + 136572 a - 10063\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a\right){x}{y}+\left(a^{4}-4a^{2}-2a+1\right){y}={x}^{3}+{x}^{2}+\left(1159a^{4}-1311a^{3}-4998a^{2}+3917a+552\right){x}+32173a^{4}-43110a^{3}-130441a^{2}+136572a-10063$ |
| 11.1-b2 |
11.1-b |
$4$ |
$15$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{5} \) |
$43.12946$ |
$(a^3-3a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$25$ |
\( 5 \) |
$1$ |
$4.396907487$ |
1.44730865 |
\( \frac{168933940112634861051}{161051} a^{4} - \frac{326043912184238254574}{161051} a^{3} - \frac{381377843583909776903}{161051} a^{2} + \frac{568280423008643207018}{161051} a - \frac{87189080412017164334}{161051} \) |
\( \bigl[a^{3} - 3 a\) , \( 1\) , \( a^{3} - 4 a + 1\) , \( -120 a^{4} - 59 a^{3} + 753 a^{2} + 417 a - 783\) , \( -1687 a^{4} - 462 a^{3} + 10333 a^{2} + 4147 a - 10436\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+{x}^{2}+\left(-120a^{4}-59a^{3}+753a^{2}+417a-783\right){x}-1687a^{4}-462a^{3}+10333a^{2}+4147a-10436$ |
| 11.1-b3 |
11.1-b |
$4$ |
$15$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{3} \) |
$43.12946$ |
$(a^3-3a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$4580.111965$ |
1.44730865 |
\( -\frac{23276749224}{1331} a^{4} + \frac{2036354170}{1331} a^{3} + \frac{162517532725}{1331} a^{2} + \frac{51601850093}{1331} a - \frac{156355149044}{1331} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{4} - 4 a^{2} - 2 a + 1\) , \( 4 a^{4} - 7 a^{3} - 19 a^{2} + 25 a - 3\) , \( 12 a^{4} - 15 a^{3} - 44 a^{2} + 47 a - 7\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-4a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(4a^{4}-7a^{3}-19a^{2}+25a-3\right){x}+12a^{4}-15a^{3}-44a^{2}+47a-7$ |
| 11.1-b4 |
11.1-b |
$4$ |
$15$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( -11 \) |
$43.12946$ |
$(a^3-3a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$13740.33589$ |
1.44730865 |
\( \frac{117598}{11} a^{4} + \frac{103030}{11} a^{3} - \frac{611217}{11} a^{2} - \frac{661252}{11} a + \frac{135283}{11} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( -a^{4} + 6 a^{2} + 2 a - 5\) , \( a^{3} - 4 a + 1\) , \( a^{4} + 3 a^{3} - 3 a^{2} - 7 a + 4\) , \( 5 a^{4} + 3 a^{3} - 22 a^{2} - 8 a + 18\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+2a-5\right){x}^{2}+\left(a^{4}+3a^{3}-3a^{2}-7a+4\right){x}+5a^{4}+3a^{3}-22a^{2}-8a+18$ |
| 17.1-a1 |
17.1-a |
$2$ |
$2$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$45.04843$ |
$(a^4-a^3-4a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.292255632$ |
$1755.507367$ |
3.37760900 |
\( -\frac{11853806}{289} a^{4} - \frac{1156127}{289} a^{3} + \frac{71086173}{289} a^{2} + \frac{22399196}{289} a - \frac{67237483}{289} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a - 3\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( 5 a^{3} - 2 a^{2} - 22 a + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 7 a - 2\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}{y}+\left(a^{4}-5a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a-3\right){x}^{2}+\left(5a^{3}-2a^{2}-22a+5\right){x}+a^{4}-2a^{3}-3a^{2}+7a-2$ |
| 17.1-a2 |
17.1-a |
$2$ |
$2$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$45.04843$ |
$(a^4-a^3-4a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.584511265$ |
$1755.507367$ |
3.37760900 |
\( \frac{150558867593}{17} a^{4} + \frac{27091861312}{17} a^{3} - \frac{896793313822}{17} a^{2} - \frac{309392244118}{17} a + \frac{846605922980}{17} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 6 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a - 3\) , \( a^{4} - 5 a^{2} - 2 a + 2\) , \( 35 a^{4} + 15 a^{3} - 172 a^{2} - 127 a + 20\) , \( -133 a^{4} - 61 a^{3} + 667 a^{2} + 497 a - 113\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-6a+2\right){x}{y}+\left(a^{4}-5a^{2}-2a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a-3\right){x}^{2}+\left(35a^{4}+15a^{3}-172a^{2}-127a+20\right){x}-133a^{4}-61a^{3}+667a^{2}+497a-113$ |
| 17.1-b1 |
17.1-b |
$2$ |
$2$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17^{2} \) |
$45.04843$ |
$(a^4-a^3-4a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.068449951$ |
$6064.820102$ |
2.73297018 |
\( -\frac{11853806}{289} a^{4} - \frac{1156127}{289} a^{3} + \frac{71086173}{289} a^{2} + \frac{22399196}{289} a - \frac{67237483}{289} \) |
\( \bigl[a^{4} - 4 a^{2} - a\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 3\) , \( a^{3} - a^{2} - 3 a + 3\) , \( 2 a^{4} + 2 a^{3} - 10 a^{2} - 12 a + 4\) , \( 2 a^{4} + 2 a^{3} - 10 a^{2} - 11 a + 1\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a\right){x}{y}+\left(a^{3}-a^{2}-3a+3\right){y}={x}^{3}+\left(a^{4}+a^{3}-6a^{2}-5a+3\right){x}^{2}+\left(2a^{4}+2a^{3}-10a^{2}-12a+4\right){x}+2a^{4}+2a^{3}-10a^{2}-11a+1$ |
| 17.1-b2 |
17.1-b |
$2$ |
$2$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$45.04843$ |
$(a^4-a^3-4a^2+a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.136899902$ |
$6064.820102$ |
2.73297018 |
\( \frac{150558867593}{17} a^{4} + \frac{27091861312}{17} a^{3} - \frac{896793313822}{17} a^{2} - \frac{309392244118}{17} a + \frac{846605922980}{17} \) |
\( \bigl[a^{4} - 4 a^{2} - a\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 3\) , \( a^{3} - a^{2} - 3 a + 3\) , \( 32 a^{4} + 27 a^{3} - 175 a^{2} - 187 a + 39\) , \( 176 a^{4} + 154 a^{3} - 912 a^{2} - 968 a + 198\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a\right){x}{y}+\left(a^{3}-a^{2}-3a+3\right){y}={x}^{3}+\left(a^{4}+a^{3}-6a^{2}-5a+3\right){x}^{2}+\left(32a^{4}+27a^{3}-175a^{2}-187a+39\right){x}+176a^{4}+154a^{3}-912a^{2}-968a+198$ |
| 27.1-a1 |
27.1-a |
$2$ |
$3$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$47.18143$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$847.3864974$ |
2.23144074 |
\( 407290876362066942 a^{4} - 585879854182775661 a^{3} - 1600968698551137044 a^{2} + 1895670869414608726 a - 283139720167859478 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{4} + 5 a^{2} + a - 1\) , \( 0\) , \( -a^{4} - 8 a^{3} + 15 a^{2} + 28 a - 6\) , \( -30 a^{4} + 78 a^{3} + 46 a^{2} - 166 a + 28\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}={x}^{3}+\left(-a^{4}+5a^{2}+a-1\right){x}^{2}+\left(-a^{4}-8a^{3}+15a^{2}+28a-6\right){x}-30a^{4}+78a^{3}+46a^{2}-166a+28$ |
| 27.1-a2 |
27.1-a |
$2$ |
$3$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$47.18143$ |
$(-a^4+5a^2+2a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$847.3864974$ |
2.23144074 |
\( 146940 a^{4} + 66227 a^{3} - 937257 a^{2} - 38423 a + 37536 \) |
\( \bigl[a\) , \( a^{4} + a^{3} - 7 a^{2} - 7 a + 5\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( 2 a^{4} + 2 a^{3} - 12 a^{2} - 11 a + 9\) , \( a^{4} + a^{3} - 5 a^{2} - 5 a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}+a^{3}-6a^{2}-5a+5\right){y}={x}^{3}+\left(a^{4}+a^{3}-7a^{2}-7a+5\right){x}^{2}+\left(2a^{4}+2a^{3}-12a^{2}-11a+9\right){x}+a^{4}+a^{3}-5a^{2}-5a+2$ |
| 27.1-b1 |
27.1-b |
$2$ |
$3$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$47.18143$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
|
\( 1 \) |
$1$ |
$146.6772538$ |
3.66544148 |
\( 407290876362066942 a^{4} - 585879854182775661 a^{3} - 1600968698551137044 a^{2} + 1895670869414608726 a - 283139720167859478 \) |
\( \bigl[a^{4} - 5 a^{2} - a + 2\) , \( -a^{4} + a^{3} + 3 a^{2} - 2 a + 2\) , \( a^{3} - 3 a + 1\) , \( -9 a^{3} - a^{2} + 18 a - 5\) , \( 2 a^{4} + 26 a^{3} - 9 a^{2} - 14 a + 3\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-2a+2\right){x}^{2}+\left(-9a^{3}-a^{2}+18a-5\right){x}+2a^{4}+26a^{3}-9a^{2}-14a+3$ |
| 27.1-b2 |
27.1-b |
$2$ |
$3$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$47.18143$ |
$(-a^4+5a^2+2a-2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
|
\( 1 \) |
$1$ |
$440.0317615$ |
3.66544148 |
\( 146940 a^{4} + 66227 a^{3} - 937257 a^{2} - 38423 a + 37536 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a^{3} - a^{2} - 3 a + 3\) , \( 19 a^{4} - 16 a^{3} - 89 a^{2} + 40 a + 31\) , \( 75 a^{4} - 102 a^{3} - 303 a^{2} + 324 a - 26\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+3\right){x}^{2}+\left(19a^{4}-16a^{3}-89a^{2}+40a+31\right){x}+75a^{4}-102a^{3}-303a^{2}+324a-26$ |
| 27.1-c1 |
27.1-c |
$2$ |
$3$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{9} \) |
$47.18143$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.373107334$ |
$737.2886048$ |
3.62197234 |
\( 407290876362066942 a^{4} - 585879854182775661 a^{3} - 1600968698551137044 a^{2} + 1895670869414608726 a - 283139720167859478 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{4} - 6 a^{2} - 3 a + 5\) , \( a^{4} - 5 a^{2} - a + 2\) , \( 37 a^{4} - 69 a^{3} - 89 a^{2} + 119 a - 12\) , \( 1574 a^{4} - 3042 a^{3} - 3558 a^{2} + 5296 a - 812\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{4}-5a^{2}-a+2\right){y}={x}^{3}+\left(a^{4}-6a^{2}-3a+5\right){x}^{2}+\left(37a^{4}-69a^{3}-89a^{2}+119a-12\right){x}+1574a^{4}-3042a^{3}-3558a^{2}+5296a-812$ |
| 27.1-c2 |
27.1-c |
$2$ |
$3$ |
5.5.144209.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$47.18143$ |
$(-a^4+5a^2+2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.124369111$ |
$2211.865814$ |
3.62197234 |
\( 146940 a^{4} + 66227 a^{3} - 937257 a^{2} - 38423 a + 37536 \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 1\) , \( a^{4} + a^{3} - 5 a^{2} - 6 a + 3\) , \( -2 a^{4} + 7 a^{3} + 5 a^{2} - 26 a + 9\) , \( -4 a^{4} + 8 a^{3} + 15 a^{2} - 28 a + 2\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{4}+a^{3}-5a^{2}-6a+3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-1\right){x}^{2}+\left(-2a^{4}+7a^{3}+5a^{2}-26a+9\right){x}-4a^{4}+8a^{3}+15a^{2}-28a+2$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
