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 |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$29.82365$ |
$(-a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$111.6491504$ |
1.49350048 |
\( \frac{7189868035226731598462231824}{43046721} a^{4} + \frac{4952838052023862893752165536}{14348907} a^{3} - \frac{4144247278847983173902029664}{14348907} a^{2} - \frac{32883257167577010709120092559}{43046721} a - \frac{10437288928816976802328054390}{43046721} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 978 a^{4} - 1249 a^{3} - 4424 a^{2} + 4612 a + 2327\) , \( -28873 a^{4} + 35329 a^{3} + 129230 a^{2} - 130011 a - 69785\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+6\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+4\right){x}^{2}+\left(978a^{4}-1249a^{3}-4424a^{2}+4612a+2327\right){x}-28873a^{4}+35329a^{3}+129230a^{2}-130011a-69785$ |
3.1-a2 |
3.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{32} \) |
$29.82365$ |
$(-a^2+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$223.2983008$ |
1.49350048 |
\( \frac{5612345015888784543060992}{1853020188851841} a^{4} + \frac{3866603197043325239325440}{617673396283947} a^{3} - \frac{3233258581638631884847573}{617673396283947} a^{2} - \frac{25663033306336515061957628}{1853020188851841} a - \frac{8145828927695352150406172}{1853020188851841} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 78 a^{4} - 94 a^{3} - 369 a^{2} + 372 a + 197\) , \( -134 a^{4} + 200 a^{3} + 466 a^{2} - 518 a - 272\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+6\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+4\right){x}^{2}+\left(78a^{4}-94a^{3}-369a^{2}+372a+197\right){x}-134a^{4}+200a^{3}+466a^{2}-518a-272$ |
3.1-a3 |
3.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$29.82365$ |
$(-a^2+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$893.1932034$ |
1.49350048 |
\( -\frac{33198692}{6561} a^{4} + \frac{22029715}{2187} a^{3} + \frac{24636235}{2187} a^{2} - \frac{111964234}{6561} a - \frac{50653123}{6561} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 3 a^{4} - 4 a^{3} - 14 a^{2} + 12 a + 12\) , \( 12 a^{4} - 14 a^{3} - 58 a^{2} + 55 a + 35\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+6\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+4\right){x}^{2}+\left(3a^{4}-4a^{3}-14a^{2}+12a+12\right){x}+12a^{4}-14a^{3}-58a^{2}+55a+35$ |
3.1-a4 |
3.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{64} \) |
$29.82365$ |
$(-a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$6.978071901$ |
1.49350048 |
\( -\frac{44061025790807839408155090358108432}{3433683820292512484657849089281} a^{4} - \frac{29484192693319885340467231541357728}{1144561273430837494885949696427} a^{3} + \frac{25479335518455763178376859990096736}{1144561273430837494885949696427} a^{2} + \frac{190470615833285713374246926035103695}{3433683820292512484657849089281} a + \frac{60660243114769730469535011714397894}{3433683820292512484657849089281} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( -342 a^{4} + 421 a^{3} + 1526 a^{2} - 1548 a - 813\) , \( -1023 a^{4} + 1339 a^{3} + 4330 a^{2} - 4529 a - 2323\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+6\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2a+4\right){x}^{2}+\left(-342a^{4}+421a^{3}+1526a^{2}-1548a-813\right){x}-1023a^{4}+1339a^{3}+4330a^{2}-4529a-2323$ |
3.1-a5 |
3.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$29.82365$ |
$(-a^2+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$446.5966017$ |
1.49350048 |
\( \frac{17583812801124161}{43046721} a^{4} - \frac{11388034497473704}{14348907} a^{3} - \frac{13038765795994792}{14348907} a^{2} + \frac{58419575550646240}{43046721} a + \frac{27146975945713360}{43046721} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 2\) , \( -5 a^{4} - 2 a^{3} + 38 a^{2} + 8 a - 71\) , \( -28 a^{4} - 8 a^{3} + 178 a^{2} + 38 a - 259\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a\right){x}^{2}+\left(-5a^{4}-2a^{3}+38a^{2}+8a-71\right){x}-28a^{4}-8a^{3}+178a^{2}+38a-259$ |
3.1-a6 |
3.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{8} \) |
$29.82365$ |
$(-a^2+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$13.95614380$ |
1.49350048 |
\( \frac{16635258169643793173504}{6561} a^{4} - \frac{10774097328296172397312}{2187} a^{3} - \frac{12336454718112027239563}{2187} a^{2} + \frac{55273903878511166850940}{6561} a + \frac{25684918726965491716972}{6561} \) |
\( \bigl[1\) , \( a^{4} - 5 a^{2} - a + 3\) , \( a^{2} - 1\) , \( -111 a^{4} + 209 a^{3} + 241 a^{2} - 350 a - 165\) , \( -1804 a^{4} + 3401 a^{3} + 3999 a^{2} - 5783 a - 2713\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-5a^{2}-a+3\right){x}^{2}+\left(-111a^{4}+209a^{3}+241a^{2}-350a-165\right){x}-1804a^{4}+3401a^{3}+3999a^{2}-5783a-2713$ |
3.1-b1 |
3.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$29.82365$ |
$(-a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$2.893745427$ |
$3.314454373$ |
1.28298716 |
\( \frac{7189868035226731598462231824}{43046721} a^{4} + \frac{4952838052023862893752165536}{14348907} a^{3} - \frac{4144247278847983173902029664}{14348907} a^{2} - \frac{32883257167577010709120092559}{43046721} a - \frac{10437288928816976802328054390}{43046721} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -5 a^{3} - 75 a^{2} - 320 a - 384\) , \( -33 a^{4} - 364 a^{3} - 1716 a^{2} - 3628 a - 2769\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a^{3}-75a^{2}-320a-384\right){x}-33a^{4}-364a^{3}-1716a^{2}-3628a-2769$ |
3.1-b2 |
3.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{32} \) |
$29.82365$ |
$(-a^2+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1.446872713$ |
$106.0625399$ |
1.28298716 |
\( \frac{5612345015888784543060992}{1853020188851841} a^{4} + \frac{3866603197043325239325440}{617673396283947} a^{3} - \frac{3233258581638631884847573}{617673396283947} a^{2} - \frac{25663033306336515061957628}{1853020188851841} a - \frac{8145828927695352150406172}{1853020188851841} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -5 a^{2} - 20 a - 24\) , \( -a^{4} - 8 a^{3} - 31 a^{2} - 60 a - 36\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-5a^{2}-20a-24\right){x}-a^{4}-8a^{3}-31a^{2}-60a-36$ |
3.1-b3 |
3.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$29.82365$ |
$(-a^2+3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.361718178$ |
$6788.002557$ |
1.28298716 |
\( -\frac{33198692}{6561} a^{4} + \frac{22029715}{2187} a^{3} + \frac{24636235}{2187} a^{2} - \frac{111964234}{6561} a - \frac{50653123}{6561} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+{x}$ |
3.1-b4 |
3.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{64} \) |
$29.82365$ |
$(-a^2+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$2.893745427$ |
$3.314454373$ |
1.28298716 |
\( -\frac{44061025790807839408155090358108432}{3433683820292512484657849089281} a^{4} - \frac{29484192693319885340467231541357728}{1144561273430837494885949696427} a^{3} + \frac{25479335518455763178376859990096736}{1144561273430837494885949696427} a^{2} + \frac{190470615833285713374246926035103695}{3433683820292512484657849089281} a + \frac{60660243114769730469535011714397894}{3433683820292512484657849089281} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a^{3} - 15 a^{2} - 40 a + 16\) , \( -13 a^{4} - 4 a^{3} + 54 a^{2} - 76 a - 183\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a^{3}-15a^{2}-40a+16\right){x}-13a^{4}-4a^{3}+54a^{2}-76a-183$ |
3.1-b5 |
3.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$29.82365$ |
$(-a^2+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.723436356$ |
$3394.001278$ |
1.28298716 |
\( \frac{17583812801124161}{43046721} a^{4} - \frac{11388034497473704}{14348907} a^{3} - \frac{13038765795994792}{14348907} a^{2} + \frac{58419575550646240}{43046721} a + \frac{27146975945713360}{43046721} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -4\) , \( -a^{2} - 4 a + 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-4{x}-a^{2}-4a+4$ |
3.1-b6 |
3.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{8} \) |
$29.82365$ |
$(-a^2+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.361718178$ |
$1697.000639$ |
1.28298716 |
\( \frac{16635258169643793173504}{6561} a^{4} - \frac{10774097328296172397312}{2187} a^{3} - \frac{12336454718112027239563}{2187} a^{2} + \frac{55273903878511166850940}{6561} a + \frac{25684918726965491716972}{6561} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a^{2} + 20 a - 64\) , \( a^{4} + 8 a^{3} - 15 a^{2} - 124 a + 220\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a^{2}+20a-64\right){x}+a^{4}+8a^{3}-15a^{2}-124a+220$ |
11.1-a1 |
11.1-a |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{4} \) |
$33.96158$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.209864983$ |
$1457.337013$ |
2.55699535 |
\( -\frac{64801139993982903601201}{14641} a^{4} + \frac{79742135469152888974129}{14641} a^{3} + \frac{290678984684285122184960}{14641} a^{2} - \frac{292899070194533892815349}{14641} a - \frac{157977896987517584455026}{14641} \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 4\) , \( a\) , \( -291 a^{4} + 574 a^{3} + 610 a^{2} - 923 a - 458\) , \( 7024 a^{4} - 13684 a^{3} - 15498 a^{2} + 23224 a + 10852\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-4\right){x}^{2}+\left(-291a^{4}+574a^{3}+610a^{2}-923a-458\right){x}+7024a^{4}-13684a^{3}-15498a^{2}+23224a+10852$ |
11.1-a2 |
11.1-a |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$33.96158$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.419729966$ |
$2914.674027$ |
2.55699535 |
\( -\frac{194960202826935862}{214358881} a^{4} + \frac{240211991646390234}{214358881} a^{3} + \frac{874044186101463078}{214358881} a^{2} - \frac{882364691646287529}{214358881} a - \frac{473469439417993593}{214358881} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 6\) , \( a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 5\) , \( 4 a^{4} + 23 a^{3} + 4 a^{2} - 93 a - 88\) , \( 45 a^{4} + 51 a^{3} - 187 a^{2} - 224 a - 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+6\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+5\right){y}={x}^{3}+\left(a^{4}-4a^{2}+a+3\right){x}^{2}+\left(4a^{4}+23a^{3}+4a^{2}-93a-88\right){x}+45a^{4}+51a^{3}-187a^{2}-224a-1$ |
11.1-a3 |
11.1-a |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$33.96158$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.209864983$ |
$5829.348054$ |
2.55699535 |
\( \frac{199999900}{14641} a^{4} - \frac{195574728}{14641} a^{3} - \frac{840036139}{14641} a^{2} + \frac{774782742}{14641} a + \frac{392874921}{14641} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 6\) , \( a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 5\) , \( -a^{4} - 2 a^{3} + 4 a^{2} + 12 a + 7\) , \( 4 a^{4} + 5 a^{3} - 15 a^{2} - 20 a - 3\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+6\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+5\right){y}={x}^{3}+\left(a^{4}-4a^{2}+a+3\right){x}^{2}+\left(-a^{4}-2a^{3}+4a^{2}+12a+7\right){x}+4a^{4}+5a^{3}-15a^{2}-20a-3$ |
11.1-a4 |
11.1-a |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{16} \) |
$33.96158$ |
$(a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.839459932$ |
$91.08356335$ |
2.55699535 |
\( \frac{476417640375476377168321}{45949729863572161} a^{4} - \frac{921552595192807794564289}{45949729863572161} a^{3} - \frac{1018805365320562990606080}{45949729863572161} a^{2} + \frac{1637467232063013399273925}{45949729863572161} a + \frac{751306184458928265884514}{45949729863572161} \) |
\( \bigl[a^{2} - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 6\) , \( -34 a^{4} - 106 a^{3} - 82 a^{2} - 9 a - 5\) , \( -1108 a^{4} - 2689 a^{3} + 484 a^{2} + 3592 a + 1217\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+6\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-34a^{4}-106a^{3}-82a^{2}-9a-5\right){x}-1108a^{4}-2689a^{3}+484a^{2}+3592a+1217$ |
11.1-b1 |
11.1-b |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( - 11^{4} \) |
$33.96158$ |
$(a^3-a^2-3a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$18.28997238$ |
1.87789849 |
\( -\frac{64801139993982903601201}{14641} a^{4} + \frac{79742135469152888974129}{14641} a^{3} + \frac{290678984684285122184960}{14641} a^{2} - \frac{292899070194533892815349}{14641} a - \frac{157977896987517584455026}{14641} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 3 a\) , \( 0\) , \( 5 a^{4} + 67 a^{3} - 14 a^{2} - 226 a - 146\) , \( 68 a^{4} + 285 a^{3} - 223 a^{2} - 1067 a - 602\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(5a^{4}+67a^{3}-14a^{2}-226a-146\right){x}+68a^{4}+285a^{3}-223a^{2}-1067a-602$ |
11.1-b2 |
11.1-b |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$33.96158$ |
$(a^3-a^2-3a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
|
\( 2 \) |
$1$ |
$585.2791162$ |
1.87789849 |
\( -\frac{194960202826935862}{214358881} a^{4} + \frac{240211991646390234}{214358881} a^{3} + \frac{874044186101463078}{214358881} a^{2} - \frac{882364691646287529}{214358881} a - \frac{473469439417993593}{214358881} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 3 a\) , \( 0\) , \( 12 a^{3} - 4 a^{2} - 36 a - 16\) , \( 6 a^{4} - 47 a^{3} + 4 a^{2} + 119 a + 39\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}={x}^{3}+\left(a^{3}-a^{2}-3a\right){x}^{2}+\left(12a^{3}-4a^{2}-36a-16\right){x}+6a^{4}-47a^{3}+4a^{2}+119a+39$ |
11.1-b3 |
11.1-b |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$33.96158$ |
$(a^3-a^2-3a+2)$ |
$0 \le r \le 1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$1170.558232$ |
1.87789849 |
\( \frac{199999900}{14641} a^{4} - \frac{195574728}{14641} a^{3} - \frac{840036139}{14641} a^{2} + \frac{774782742}{14641} a + \frac{392874921}{14641} \) |
\( \bigl[a^{2} - 1\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 7\) , \( a^{4} - 4 a^{2} + 3\) , \( a^{4} - 2 a^{3} - 5 a^{2} + 6 a + 7\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-6a-7\right){x}^{2}+\left(a^{4}-2a^{3}-5a^{2}+6a+7\right){x}+a^{4}-2a^{3}-3a^{2}+5a$ |
11.1-b4 |
11.1-b |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
11.1 |
\( 11 \) |
\( 11^{16} \) |
$33.96158$ |
$(a^3-a^2-3a+2)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$292.6395581$ |
1.87789849 |
\( \frac{476417640375476377168321}{45949729863572161} a^{4} - \frac{921552595192807794564289}{45949729863572161} a^{3} - \frac{1018805365320562990606080}{45949729863572161} a^{2} + \frac{1637467232063013399273925}{45949729863572161} a + \frac{751306184458928265884514}{45949729863572161} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 3\) , \( a^{4} - 5 a^{2} + 4\) , \( 19 a^{4} - 67 a^{3} - 120 a^{2} + 207 a + 88\) , \( -36 a^{4} - 539 a^{3} - 321 a^{2} + 1448 a + 587\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4a+3\right){x}^{2}+\left(19a^{4}-67a^{3}-120a^{2}+207a+88\right){x}-36a^{4}-539a^{3}-321a^{2}+1448a+587$ |
15.1-a1 |
15.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{4} \cdot 5^{4} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$225.2008724$ |
1.50622557 |
\( -\frac{15389896220497090102101210740429393}{50625} a^{4} + \frac{6312748790805023532092019014193904}{16875} a^{3} + \frac{184092427599994075286402603282732}{135} a^{2} - \frac{69561645181256648368785973700909857}{50625} a - \frac{37519140001683296502867018256185481}{50625} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{4} - 4 a^{2} + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( -129 a^{4} - 18 a^{3} + 812 a^{2} + 114 a - 1295\) , \( -1383 a^{4} + 867 a^{3} + 6791 a^{2} - 3574 a - 5877\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+4a+6\right){y}={x}^{3}+\left(a^{4}-4a^{2}+3\right){x}^{2}+\left(-129a^{4}-18a^{3}+812a^{2}+114a-1295\right){x}-1383a^{4}+867a^{3}+6791a^{2}-3574a-5877$ |
15.1-a2 |
15.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{5} \) |
$1$ |
$14.07505452$ |
1.50622557 |
\( \frac{80464916007546305131892520001046417}{6568408355712890625} a^{4} + \frac{55429346280690132389667409076478224}{2189469451904296875} a^{3} - \frac{371040528095033839452431598188588}{17515755615234375} a^{2} - \frac{368010740589323725200893981996043167}{6568408355712890625} a - \frac{116808209503189306818905239743620711}{6568408355712890625} \) |
\( \bigl[a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( 75 a^{4} - 147 a^{3} - 348 a^{2} + 530 a + 208\) , \( -991 a^{4} + 887 a^{3} + 4408 a^{2} - 3273 a - 2377\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-3\right){x}^{2}+\left(75a^{4}-147a^{3}-348a^{2}+530a+208\right){x}-991a^{4}+887a^{3}+4408a^{2}-3273a-2377$ |
15.1-a3 |
15.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$450.4017449$ |
1.50622557 |
\( -\frac{612030007956284658845698}{2562890625} a^{4} + \frac{251047360103669915791319}{854296875} a^{3} + \frac{7321043353858505394772}{6834375} a^{2} - \frac{2766348970846187227553552}{2562890625} a - \frac{1492072668359949650949416}{2562890625} \) |
\( \bigl[a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( 90 a^{4} - 112 a^{3} - 383 a^{2} + 405 a + 138\) , \( -869 a^{4} + 1023 a^{3} + 3943 a^{2} - 3749 a - 2285\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-3\right){x}^{2}+\left(90a^{4}-112a^{3}-383a^{2}+405a+138\right){x}-869a^{4}+1023a^{3}+3943a^{2}-3749a-2285$ |
15.1-a4 |
15.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1801.606979$ |
1.50622557 |
\( -\frac{17156804}{225} a^{4} + \frac{2271487}{75} a^{3} + \frac{1342159}{3} a^{2} - \frac{22669771}{225} a - \frac{129471568}{225} \) |
\( \bigl[a + 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{2} - 2\) , \( -2 a^{3} + 2 a^{2} + 5 a - 2\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+4a^{2}-2a-3\right){x}^{2}+\left(-2a^{3}+2a^{2}+5a-2\right){x}-a^{4}+a^{3}+4a^{2}-2a-4$ |
15.1-a5 |
15.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$900.8034899$ |
1.50622557 |
\( \frac{1834535325830018}{50625} a^{4} - \frac{245905361184529}{16875} a^{3} - \frac{28562103469112}{135} a^{2} + \frac{2472941308147357}{50625} a + \frac{13682736706682356}{50625} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 5\) , \( 0\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 28 a^{4} + 38 a^{3} - 108 a^{2} - 167 a - 46\) , \( 160 a^{4} + 248 a^{3} - 596 a^{2} - 1085 a - 328\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+5\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(28a^{4}+38a^{3}-108a^{2}-167a-46\right){x}+160a^{4}+248a^{3}-596a^{2}-1085a-328$ |
15.1-a6 |
15.1-a |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{2} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$28.15010905$ |
1.50622557 |
\( \frac{1780112723050931045737154}{225} a^{4} - \frac{238701200978374567424887}{75} a^{3} - \frac{138568029847481079481636}{3} a^{2} + \frac{2400622468903683011892496}{225} a + \frac{13275179570859946573387768}{225} \) |
\( \bigl[a^{3} - 2 a - 1\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -58 a^{4} + 142 a^{3} + 22 a^{2} - 104 a - 80\) , \( -2600 a^{4} + 4786 a^{3} + 6601 a^{2} - 8999 a - 4418\bigr] \) |
${y}^2+\left(a^{3}-2a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a\right){x}^{2}+\left(-58a^{4}+142a^{3}+22a^{2}-104a-80\right){x}-2600a^{4}+4786a^{3}+6601a^{2}-8999a-4418$ |
15.1-b1 |
15.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{4} \cdot 5^{4} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{3} \) |
$1$ |
$2.735062817$ |
1.17075825 |
\( -\frac{15389896220497090102101210740429393}{50625} a^{4} + \frac{6312748790805023532092019014193904}{16875} a^{3} + \frac{184092427599994075286402603282732}{135} a^{2} - \frac{69561645181256648368785973700909857}{50625} a - \frac{37519140001683296502867018256185481}{50625} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{4} + 4 a^{2} - a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 248 a^{4} - 250 a^{3} - 1157 a^{2} + 958 a + 541\) , \( 4001 a^{4} - 4533 a^{3} - 18282 a^{2} + 17017 a + 9402\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a-1\right){x}^{2}+\left(248a^{4}-250a^{3}-1157a^{2}+958a+541\right){x}+4001a^{4}-4533a^{3}-18282a^{2}+17017a+9402$ |
15.1-b2 |
15.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{5} \) |
$1$ |
$2.735062817$ |
1.17075825 |
\( \frac{80464916007546305131892520001046417}{6568408355712890625} a^{4} + \frac{55429346280690132389667409076478224}{2189469451904296875} a^{3} - \frac{371040528095033839452431598188588}{17515755615234375} a^{2} - \frac{368010740589323725200893981996043167}{6568408355712890625} a - \frac{116808209503189306818905239743620711}{6568408355712890625} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{4} + 4 a^{2} - a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -72 a^{4} - 200 a^{3} + 93 a^{2} + 478 a + 161\) , \( -1327 a^{4} - 2985 a^{3} + 2050 a^{2} + 6735 a + 2224\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a-1\right){x}^{2}+\left(-72a^{4}-200a^{3}+93a^{2}+478a+161\right){x}-1327a^{4}-2985a^{3}+2050a^{2}+6735a+2224$ |
15.1-b3 |
15.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$87.52201017$ |
1.17075825 |
\( -\frac{612030007956284658845698}{2562890625} a^{4} + \frac{251047360103669915791319}{854296875} a^{3} + \frac{7321043353858505394772}{6834375} a^{2} - \frac{2766348970846187227553552}{2562890625} a - \frac{1492072668359949650949416}{2562890625} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{4} + 4 a^{2} - a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( 8 a^{4} - 25 a^{3} - 52 a^{2} + 78 a + 31\) , \( 53 a^{4} - 153 a^{3} - 324 a^{2} + 482 a + 237\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a-1\right){x}^{2}+\left(8a^{4}-25a^{3}-52a^{2}+78a+31\right){x}+53a^{4}-153a^{3}-324a^{2}+482a+237$ |
15.1-b4 |
15.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5601.408651$ |
1.17075825 |
\( -\frac{17156804}{225} a^{4} + \frac{2271487}{75} a^{3} + \frac{1342159}{3} a^{2} - \frac{22669771}{225} a - \frac{129471568}{225} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{4} + 4 a^{2} - a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -2 a^{4} + 8 a^{2} - 2 a - 4\) , \( -a^{4} + 4 a^{2} - a - 2\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a-1\right){x}^{2}+\left(-2a^{4}+8a^{2}-2a-4\right){x}-a^{4}+4a^{2}-a-2$ |
15.1-b5 |
15.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$2800.704325$ |
1.17075825 |
\( \frac{1834535325830018}{50625} a^{4} - \frac{245905361184529}{16875} a^{3} - \frac{28562103469112}{135} a^{2} + \frac{2472941308147357}{50625} a + \frac{13682736706682356}{50625} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{4} + 4 a^{2} - a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -2 a^{4} + 8 a^{2} - 2 a - 9\) , \( a^{4} - 5 a^{3} - 8 a^{2} + 15 a + 9\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a-1\right){x}^{2}+\left(-2a^{4}+8a^{2}-2a-9\right){x}+a^{4}-5a^{3}-8a^{2}+15a+9$ |
15.1-b6 |
15.1-b |
$6$ |
$8$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
15.1 |
\( 3 \cdot 5 \) |
\( - 3^{2} \cdot 5^{2} \) |
$35.03142$ |
$(-a^2+3), (-a^4-2a^3+2a^2+5a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1400.352162$ |
1.17075825 |
\( \frac{1780112723050931045737154}{225} a^{4} - \frac{238701200978374567424887}{75} a^{3} - \frac{138568029847481079481636}{3} a^{2} + \frac{2400622468903683011892496}{225} a + \frac{13275179570859946573387768}{225} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{4} + 4 a^{2} - a - 1\) , \( a^{4} - 4 a^{2} + a + 3\) , \( -12 a^{4} + 25 a^{3} + 68 a^{2} - 82 a - 129\) , \( 37 a^{4} - 77 a^{3} - 220 a^{2} + 252 a + 405\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a-1\right){x}^{2}+\left(-12a^{4}+25a^{3}+68a^{2}-82a-129\right){x}+37a^{4}-77a^{3}-220a^{2}+252a+405$ |
25.1-a1 |
25.1-a |
$2$ |
$3$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$36.86741$ |
$(-a^4-2a^3+2a^2+5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.155739950$ |
$318.4448926$ |
3.31706719 |
\( \frac{7104562192214}{125} a^{4} + \frac{10722502130299}{125} a^{3} - 211554360729 a^{2} - \frac{47015436445339}{125} a - \frac{14121926205712}{125} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{4} + 6 a^{2} - 6\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 7 a^{4} + 3 a^{3} - 26 a^{2} - 7 a + 10\) , \( 8 a^{4} + 21 a^{3} - 15 a^{2} - 62 a - 23\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-6\right){x}^{2}+\left(7a^{4}+3a^{3}-26a^{2}-7a+10\right){x}+8a^{4}+21a^{3}-15a^{2}-62a-23$ |
25.1-a2 |
25.1-a |
$2$ |
$3$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{7} \) |
$36.86741$ |
$(-a^4-2a^3+2a^2+5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.051913316$ |
$955.3346779$ |
3.31706719 |
\( \frac{5096}{5} a^{4} + \frac{2861}{5} a^{3} - 3248 a^{2} - \frac{20776}{5} a - \frac{5848}{5} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 4\) , \( -a^{4} + 4 a^{2} + a - 3\) , \( a\) , \( -a^{4} + 2 a^{3} + a^{2} - 3 a\) , \( 2 a^{4} - 3 a^{3} - 5 a^{2} + 4 a + 2\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+4\right){x}{y}+a{y}={x}^{3}+\left(-a^{4}+4a^{2}+a-3\right){x}^{2}+\left(-a^{4}+2a^{3}+a^{2}-3a\right){x}+2a^{4}-3a^{3}-5a^{2}+4a+2$ |
25.1-b1 |
25.1-b |
$2$ |
$3$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{9} \) |
$36.86741$ |
$(-a^4-2a^3+2a^2+5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.070216284$ |
$954.6019571$ |
2.24155870 |
\( \frac{7104562192214}{125} a^{4} + \frac{10722502130299}{125} a^{3} - 211554360729 a^{2} - \frac{47015436445339}{125} a - \frac{14121926205712}{125} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{4} + a^{3} + 5 a^{2} - 3 a - 5\) , \( a^{3} + a^{2} - 2 a - 3\) , \( -4 a^{4} - 7 a^{3} + 7 a^{2} + 14 a + 3\) , \( 142 a^{4} + 292 a^{3} - 245 a^{2} - 645 a - 206\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{4}+a^{3}+5a^{2}-3a-5\right){x}^{2}+\left(-4a^{4}-7a^{3}+7a^{2}+14a+3\right){x}+142a^{4}+292a^{3}-245a^{2}-645a-206$ |
25.1-b2 |
25.1-b |
$2$ |
$3$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{7} \) |
$36.86741$ |
$(-a^4-2a^3+2a^2+5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.023405428$ |
$2863.805871$ |
2.24155870 |
\( \frac{5096}{5} a^{4} + \frac{2861}{5} a^{3} - 3248 a^{2} - \frac{20776}{5} a - \frac{5848}{5} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 2 a - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - 2 a - 3\) , \( 2 a^{4} - 12 a^{2} + a + 15\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-2a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+1\right){x}^{2}+\left(-a^{4}+a^{3}+4a^{2}-2a-3\right){x}+2a^{4}-12a^{2}+a+15$ |
27.1-a1 |
27.1-a |
$1$ |
$1$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$37.15224$ |
$(-a^2+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$638.0241347$ |
2.13366906 |
\( 5971545 a^{4} - 7541907 a^{3} - 26845037 a^{2} + 27768483 a + 14867787 \) |
\( \bigl[a + 1\) , \( -a^{4} + a^{3} + 6 a^{2} - 3 a - 7\) , \( 1\) , \( 3 a^{4} + a^{3} - 15 a^{2} - 6 a + 10\) , \( -3 a^{4} - 5 a^{3} + 9 a^{2} + 15 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-3a-7\right){x}^{2}+\left(3a^{4}+a^{3}-15a^{2}-6a+10\right){x}-3a^{4}-5a^{3}+9a^{2}+15a+1$ |
27.1-b1 |
27.1-b |
$1$ |
$1$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$37.15224$ |
$(-a^2+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$561.7947183$ |
1.87874399 |
\( 3420535691 a^{4} - 6646097797 a^{3} - 7609851087 a^{2} + 11365399202 a + 5281322670 \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 2 a - 3\) , \( 1\) , \( -2 a^{4} + 6 a^{3} + 15 a^{2} - 16 a - 21\) , \( -4 a^{4} + 6 a^{3} + 29 a^{2} - 16 a - 42\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+4a+3\right){x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-2a-3\right){x}^{2}+\left(-2a^{4}+6a^{3}+15a^{2}-16a-21\right){x}-4a^{4}+6a^{3}+29a^{2}-16a-42$ |
27.1-c1 |
27.1-c |
$1$ |
$1$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$37.15224$ |
$(-a^2+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$428.7601590$ |
1.43385216 |
\( 74908710 a^{4} - 145576809 a^{3} - 166586870 a^{2} + 248936745 a + 115550715 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + a^{3} + 6 a^{2} - 3 a - 7\) , \( a^{2} - 1\) , \( -a^{4} - 2 a^{3} + 4 a + 5\) , \( a^{4} + 3 a^{3} - a^{2} - 7 a - 4\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-3a-7\right){x}^{2}+\left(-a^{4}-2a^{3}+4a+5\right){x}+a^{4}+3a^{3}-a^{2}-7a-4$ |
27.1-d1 |
27.1-d |
$1$ |
$1$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$37.15224$ |
$(-a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.014958309$ |
$3875.734617$ |
2.90815631 |
\( 3420535691 a^{4} - 6646097797 a^{3} - 7609851087 a^{2} + 11365399202 a + 5281322670 \) |
\( \bigl[a^{4} - 5 a^{2} + 5\) , \( a^{4} - 5 a^{2} + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 6\) , \( a^{4} + a^{3} - 10 a^{2} + 18\) , \( 5 a^{4} - a^{3} - 24 a^{2} - a + 23\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+5\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+3a+6\right){y}={x}^{3}+\left(a^{4}-5a^{2}+5\right){x}^{2}+\left(a^{4}+a^{3}-10a^{2}+18\right){x}+5a^{4}-a^{3}-24a^{2}-a+23$ |
27.1-e1 |
27.1-e |
$1$ |
$1$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{11} \) |
$37.15224$ |
$(-a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$0.352665335$ |
$460.6675804$ |
2.71650420 |
\( 5971545 a^{4} - 7541907 a^{3} - 26845037 a^{2} + 27768483 a + 14867787 \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - 2 a^{3} - 6 a^{2} + 7 a + 9\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -6 a^{4} - 18 a^{3} + a^{2} + 41 a + 30\) , \( -59 a^{4} - 126 a^{3} + 94 a^{2} + 277 a + 99\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-6a^{2}+7a+9\right){x}^{2}+\left(-6a^{4}-18a^{3}+a^{2}+41a+30\right){x}-59a^{4}-126a^{3}+94a^{2}+277a+99$ |
27.1-f1 |
27.1-f |
$1$ |
$1$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$37.15224$ |
$(-a^2+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 3 \) |
$0.002724823$ |
$17258.69452$ |
2.35899788 |
\( 74908710 a^{4} - 145576809 a^{3} - 166586870 a^{2} + 248936745 a + 115550715 \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 5\) , \( a^{2} - 1\) , \( a^{2} + a - 1\) , \( -5 a^{4} + 6 a^{3} + 22 a^{2} - 23 a - 11\) , \( -51 a^{4} + 62 a^{3} + 228 a^{2} - 229 a - 124\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+4a+5\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(-5a^{4}+6a^{3}+22a^{2}-23a-11\right){x}-51a^{4}+62a^{3}+228a^{2}-229a-124$ |
33.1-a1 |
33.1-a |
$2$ |
$2$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{4} \cdot 11^{4} \) |
$37.90530$ |
$(-a^2+3), (a^3-a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$185.7626310$ |
1.24244823 |
\( -\frac{689946655001}{1185921} a^{4} + \frac{97551617131}{395307} a^{3} + \frac{1331574070630}{395307} a^{2} - \frac{951264428458}{1185921} a - \frac{5090492813704}{1185921} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{4} + a^{3} + 6 a^{2} - 3 a - 7\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 4\) , \( 9 a^{3} + 6 a^{2} - 26 a - 8\) , \( 2 a^{4} + 10 a^{3} + a^{2} - 25 a - 13\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+4\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-3a-7\right){x}^{2}+\left(9a^{3}+6a^{2}-26a-8\right){x}+2a^{4}+10a^{3}+a^{2}-25a-13$ |
33.1-a2 |
33.1-a |
$2$ |
$2$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{8} \cdot 11^{2} \) |
$37.90530$ |
$(-a^2+3), (a^3-a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$92.88131554$ |
1.24244823 |
\( \frac{1575796951026290471}{793881} a^{4} - \frac{211689533367899416}{264627} a^{3} - \frac{3065686215915753391}{264627} a^{2} + \frac{2126569645502210011}{793881} a + \frac{11747056248779259589}{793881} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( -a^{4} + a^{3} + 6 a^{2} - 3 a - 7\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 4\) , \( 20 a^{4} - a^{3} - 79 a^{2} + 9 a + 17\) , \( 43 a^{4} + 6 a^{3} - 166 a^{2} - 15 a + 18\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+4\right){y}={x}^{3}+\left(-a^{4}+a^{3}+6a^{2}-3a-7\right){x}^{2}+\left(20a^{4}-a^{3}-79a^{2}+9a+17\right){x}+43a^{4}+6a^{3}-166a^{2}-15a+18$ |
33.1-b1 |
33.1-b |
$1$ |
$1$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{13} \cdot 11 \) |
$37.90530$ |
$(-a^2+3), (a^3-a^2-3a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$543.0525150$ |
1.81606664 |
\( \frac{70326015817667}{17537553} a^{4} + \frac{35385078947300}{5845851} a^{3} - \frac{87254456187883}{5845851} a^{2} - \frac{465454958190215}{17537553} a - \frac{139799411135147}{17537553} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 4\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 4\) , \( 2 a^{4} - 2 a^{3} - 11 a^{2} + 6 a + 11\) , \( a^{4} - 4 a^{2} + 2\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+2a+4\right){x}^{2}+\left(2a^{4}-2a^{3}-11a^{2}+6a+11\right){x}+a^{4}-4a^{2}+2$ |
33.1-c1 |
33.1-c |
$1$ |
$1$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{13} \cdot 11 \) |
$37.90530$ |
$(-a^2+3), (a^3-a^2-3a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 13 \) |
$0.006943956$ |
$2113.983397$ |
3.19089032 |
\( \frac{70326015817667}{17537553} a^{4} + \frac{35385078947300}{5845851} a^{3} - \frac{87254456187883}{5845851} a^{2} - \frac{465454958190215}{17537553} a - \frac{139799411135147}{17537553} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{4} + 4 a^{2} - a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 3\) , \( 4 a^{4} - 4 a^{3} - 19 a^{2} + 14 a + 14\) , \( a^{4} - 4 a^{2} + a + 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+4a+3\right){y}={x}^{3}+\left(-a^{4}+4a^{2}-a-3\right){x}^{2}+\left(4a^{4}-4a^{3}-19a^{2}+14a+14\right){x}+a^{4}-4a^{2}+a+2$ |
33.1-d1 |
33.1-d |
$2$ |
$2$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{4} \cdot 11^{4} \) |
$37.90530$ |
$(-a^2+3), (a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.007042999$ |
$8047.555257$ |
3.79089362 |
\( -\frac{689946655001}{1185921} a^{4} + \frac{97551617131}{395307} a^{3} + \frac{1331574070630}{395307} a^{2} - \frac{951264428458}{1185921} a - \frac{5090492813704}{1185921} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a\) , \( a^{3} - 3 a - 1\) , \( -3 a^{4} + 5 a^{3} + 21 a^{2} - 14 a - 27\) , \( 5 a^{4} + 2 a^{3} - 25 a^{2} - 4 a + 29\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}-a{x}^{2}+\left(-3a^{4}+5a^{3}+21a^{2}-14a-27\right){x}+5a^{4}+2a^{3}-25a^{2}-4a+29$ |
33.1-d2 |
33.1-d |
$2$ |
$2$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( - 3^{8} \cdot 11^{2} \) |
$37.90530$ |
$(-a^2+3), (a^3-a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.014085999$ |
$4023.777628$ |
3.79089362 |
\( \frac{1575796951026290471}{793881} a^{4} - \frac{211689533367899416}{264627} a^{3} - \frac{3065686215915753391}{264627} a^{2} + \frac{2126569645502210011}{793881} a + \frac{11747056248779259589}{793881} \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a\) , \( a^{3} - 3 a - 1\) , \( -43 a^{4} + 20 a^{3} + 266 a^{2} - 59 a - 362\) , \( 322 a^{4} - 114 a^{3} - 1857 a^{2} + 396 a + 2353\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}-a{x}^{2}+\left(-43a^{4}+20a^{3}+266a^{2}-59a-362\right){x}+322a^{4}-114a^{3}-1857a^{2}+396a+2353$ |
41.1-a1 |
41.1-a |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( 41^{8} \) |
$38.73709$ |
$(a^4-4a^2+a+4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$75.26671791$ |
2.01364505 |
\( \frac{10098050851297890767555}{7984925229121} a^{4} + \frac{20227030168709819545088}{7984925229121} a^{3} - \frac{17543952355452858983883}{7984925229121} a^{2} - \frac{44915610066644249105473}{7984925229121} a - \frac{14168791526536387456341}{7984925229121} \) |
\( \bigl[a^{4} - 4 a^{2} + a + 3\) , \( a^{4} - 5 a^{2} + 3\) , \( a^{4} - 4 a^{2} + 2\) , \( -81 a^{4} + 67 a^{3} + 498 a^{2} - 235 a - 737\) , \( -1062 a^{4} + 275 a^{3} + 5999 a^{2} - 764 a - 7078\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+a+3\right){x}{y}+\left(a^{4}-4a^{2}+2\right){y}={x}^{3}+\left(a^{4}-5a^{2}+3\right){x}^{2}+\left(-81a^{4}+67a^{3}+498a^{2}-235a-737\right){x}-1062a^{4}+275a^{3}+5999a^{2}-764a-7078$ |
41.1-a2 |
41.1-a |
$4$ |
$4$ |
5.5.89417.1 |
$5$ |
$[5, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$38.73709$ |
$(a^4-4a^2+a+4)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4817.069946$ |
2.01364505 |
\( \frac{240520928}{1681} a^{4} + \frac{362416590}{1681} a^{3} - \frac{895769633}{1681} a^{2} - \frac{1588509281}{1681} a - \frac{474244383}{1681} \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( a^{3} - 2 a - 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -5 a^{4} + 8 a^{3} + 23 a^{2} - 31 a - 11\) , \( -49 a^{4} + 60 a^{3} + 219 a^{2} - 220 a - 119\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-2a-1\right){x}^{2}+\left(-5a^{4}+8a^{3}+23a^{2}-31a-11\right){x}-49a^{4}+60a^{3}+219a^{2}-220a-119$ |
*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.