| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 7.1-a1 |
7.1-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11015.21487$ |
1.21715 |
\( -\frac{1791563}{49} a^{5} + \frac{7166395}{49} a^{4} - \frac{2453992}{49} a^{3} - \frac{16901335}{49} a^{2} + \frac{15464328}{49} a - \frac{1410279}{49} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + a^{2} - a + 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 8 a^{2} - 2 a + 6\) , \( a^{2} - 2\) , \( -a^{5} + 2 a^{4} + 9 a^{3} - 12 a^{2} - 17 a + 18\) , \( -a^{5} + 3 a^{4} + 7 a^{3} - 12 a^{2} - 10 a + 12\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+a^{2}-a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-8a^{2}-2a+6\right){x}^{2}+\left(-a^{5}+2a^{4}+9a^{3}-12a^{2}-17a+18\right){x}-a^{5}+3a^{4}+7a^{3}-12a^{2}-10a+12$ |
| 7.1-a2 |
7.1-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( 7^{8} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2753.803719$ |
1.21715 |
\( -\frac{6808447220731}{343} a^{5} + \frac{25110461093918}{343} a^{4} - \frac{255264165124}{49} a^{3} - \frac{9161099643674}{49} a^{2} + \frac{40005374502859}{343} a + \frac{5043045079321}{343} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + a - 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 7 a^{2} - 4 a + 3\) , \( a^{2} - 1\) , \( -10 a^{5} + 25 a^{4} + 27 a^{3} - 65 a^{2} - a - 37\) , \( -3 a^{5} + 7 a^{4} - 3 a^{3} + 24 a^{2} + 25 a - 147\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-7a^{2}-4a+3\right){x}^{2}+\left(-10a^{5}+25a^{4}+27a^{3}-65a^{2}-a-37\right){x}-3a^{5}+7a^{4}-3a^{3}+24a^{2}+25a-147$ |
| 7.1-a3 |
7.1-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$172.1127324$ |
1.21715 |
\( \frac{559397469874345863}{7} a^{5} + \frac{186193611629756651}{7} a^{4} - 417383753370667154 a^{3} - 174530750288065719 a^{2} + \frac{2741687230117180432}{7} a + \frac{239882528420447896}{7} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 2 a\) , \( a + 1\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 5 a^{2} - 2 a\) , \( 1163 a^{5} - 24 a^{4} - 6593 a^{3} - 1732 a^{2} + 6061 a - 533\) , \( -41920 a^{5} - 2789 a^{4} + 244349 a^{3} + 81760 a^{2} - 238081 a - 14710\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-2a\right){x}{y}+\left(a^{5}-2a^{4}-2a^{3}+5a^{2}-2a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1163a^{5}-24a^{4}-6593a^{3}-1732a^{2}+6061a-533\right){x}-41920a^{5}-2789a^{4}+244349a^{3}+81760a^{2}-238081a-14710$ |
| 7.1-a4 |
7.1-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( 7^{16} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$43.02818311$ |
1.21715 |
\( -\frac{112621865305044987921809}{117649} a^{5} + \frac{234809319873746457270272}{117649} a^{4} + \frac{655787555635779476691259}{117649} a^{3} - \frac{1181918266837223195726037}{117649} a^{2} - \frac{1025831888427468187613336}{117649} a + \frac{1325970015560148997468622}{117649} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + a^{2} - a + 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 8 a^{2} - 2 a + 6\) , \( a^{2} - 2\) , \( 29 a^{5} - 13 a^{4} - 146 a^{3} - 22 a^{2} + 113 a + 18\) , \( 177 a^{5} - 30 a^{4} - 990 a^{3} - 249 a^{2} + 891 a + 49\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+a^{2}-a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-8a^{2}-2a+6\right){x}^{2}+\left(29a^{5}-13a^{4}-146a^{3}-22a^{2}+113a+18\right){x}+177a^{5}-30a^{4}-990a^{3}-249a^{2}+891a+49$ |
| 7.1-a5 |
7.1-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$688.4509298$ |
1.21715 |
\( -\frac{203442160742265836111311}{49} a^{5} + \frac{754939116457579934341120}{49} a^{4} - \frac{70918941964796608216091}{49} a^{3} - \frac{1913091408632068298504203}{49} a^{2} + \frac{1238551091877646917232536}{49} a + \frac{118914358788506027626050}{49} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 2 a\) , \( a + 1\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 5 a^{2} - 2 a\) , \( 133 a^{5} - 144 a^{4} - 648 a^{3} + 438 a^{2} + 631 a - 473\) , \( -87 a^{5} - 1216 a^{4} + 1168 a^{3} + 6099 a^{2} - 451 a - 4783\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-2a\right){x}{y}+\left(a^{5}-2a^{4}-2a^{3}+5a^{2}-2a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(133a^{5}-144a^{4}-648a^{3}+438a^{2}+631a-473\right){x}-87a^{5}-1216a^{4}+1168a^{3}+6099a^{2}-451a-4783$ |
| 7.1-a6 |
7.1-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$10.75704577$ |
1.21715 |
\( -\frac{1307780824025356872024765295948965037006665607}{7} a^{5} + \frac{4852951306689182093152206038520079788667830037}{7} a^{4} - 65126571056091535976357513219578497247532910 a^{3} - 1756837878700362061740707440950803215540288329 a^{2} + \frac{7961738912049866844077158263606893208018336752}{7} a + \frac{764413421276477386339801659357910076498899480}{7} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 10 a^{2} - 2 a - 3\) , \( a^{4} - 5 a^{2} + 4\) , \( -140 a^{5} + 466 a^{4} + 113 a^{3} - 1407 a^{2} + 832 a + 55\) , \( 6112 a^{5} - 20517 a^{4} - 7299 a^{3} + 65732 a^{2} - 28671 a - 12655\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+10a^{2}-2a-3\right){x}^{2}+\left(-140a^{5}+466a^{4}+113a^{3}-1407a^{2}+832a+55\right){x}+6112a^{5}-20517a^{4}-7299a^{3}+65732a^{2}-28671a-12655$ |
| 7.1-b1 |
7.1-b |
$1$ |
$1$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{11} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1912.003895$ |
1.69016 |
\( \frac{149058165}{2401} a^{5} + \frac{42596796}{2401} a^{4} - \frac{798394484}{2401} a^{3} - \frac{324858396}{2401} a^{2} + \frac{752486768}{2401} a + \frac{64104881}{2401} \) |
\( \bigl[a^{5} - 2 a^{4} - 2 a^{3} + 5 a^{2} - 3 a - 1\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 6 a^{2} - 5 a - 4\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 3 a^{5} - 12 a^{4} - 2 a^{3} + 39 a^{2} - 17 a\) , \( 8 a^{5} - 29 a^{4} - a^{3} + 87 a^{2} - 66 a - 2\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-2a^{3}+5a^{2}-3a-1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-2a^{3}+6a^{2}-5a-4\right){x}^{2}+\left(3a^{5}-12a^{4}-2a^{3}+39a^{2}-17a\right){x}+8a^{5}-29a^{4}-a^{3}+87a^{2}-66a-2$ |
| 7.1-c1 |
7.1-c |
$1$ |
$1$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{11} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 11 \) |
$0.008193862$ |
$4984.021577$ |
2.38261 |
\( \frac{149058165}{2401} a^{5} + \frac{42596796}{2401} a^{4} - \frac{798394484}{2401} a^{3} - \frac{324858396}{2401} a^{2} + \frac{752486768}{2401} a + \frac{64104881}{2401} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 7 a^{2} - 4\) , \( -7 a^{5} + 24 a^{4} + 2 a^{3} - 63 a^{2} + 30 a + 12\) , \( -7 a^{5} + 22 a^{4} + 3 a^{3} - 54 a^{2} + 34 a\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+7a^{2}-4\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+a+1\right){x}^{2}+\left(-7a^{5}+24a^{4}+2a^{3}-63a^{2}+30a+12\right){x}-7a^{5}+22a^{4}+3a^{3}-54a^{2}+34a$ |
| 7.1-d1 |
7.1-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.505543470$ |
$15670.53055$ |
2.62611 |
\( -\frac{1791563}{49} a^{5} + \frac{7166395}{49} a^{4} - \frac{2453992}{49} a^{3} - \frac{16901335}{49} a^{2} + \frac{15464328}{49} a - \frac{1410279}{49} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( 6 a^{3} - 6 a^{2} - 19 a + 16\) , \( 2 a^{5} + 5 a^{4} - 13 a^{3} - 24 a^{2} + 14 a + 14\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-12a^{2}-a+6\right){x}^{2}+\left(6a^{3}-6a^{2}-19a+16\right){x}+2a^{5}+5a^{4}-13a^{3}-24a^{2}+14a+14$ |
| 7.1-d2 |
7.1-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( 7^{8} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.011086940$ |
$3917.632638$ |
2.62611 |
\( -\frac{6808447220731}{343} a^{5} + \frac{25110461093918}{343} a^{4} - \frac{255264165124}{49} a^{3} - \frac{9161099643674}{49} a^{2} + \frac{40005374502859}{343} a + \frac{5043045079321}{343} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( 6 a^{3} - 6 a^{2} - 19 a + 11\) , \( a^{5} - 2 a^{3} - 4 a^{2} - 5 a + 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-12a^{2}-a+6\right){x}^{2}+\left(6a^{3}-6a^{2}-19a+11\right){x}+a^{5}-2a^{3}-4a^{2}-5a+5$ |
| 7.1-d3 |
7.1-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$4.044347761$ |
$0.956453280$ |
2.62611 |
\( \frac{559397469874345863}{7} a^{5} + \frac{186193611629756651}{7} a^{4} - 417383753370667154 a^{3} - 174530750288065719 a^{2} + \frac{2741687230117180432}{7} a + \frac{239882528420447896}{7} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -205 a^{5} + 445 a^{4} + 901 a^{3} - 1561 a^{2} - 1329 a - 94\) , \( -3408 a^{5} + 5120 a^{4} + 17678 a^{3} - 17421 a^{2} - 27884 a - 2251\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-12a^{2}-a+6\right){x}^{2}+\left(-205a^{5}+445a^{4}+901a^{3}-1561a^{2}-1329a-94\right){x}-3408a^{5}+5120a^{4}+17678a^{3}-17421a^{2}-27884a-2251$ |
| 7.1-d4 |
7.1-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( 7^{16} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.505543470$ |
$979.4081595$ |
2.62611 |
\( -\frac{112621865305044987921809}{117649} a^{5} + \frac{234809319873746457270272}{117649} a^{4} + \frac{655787555635779476691259}{117649} a^{3} - \frac{1181918266837223195726037}{117649} a^{2} - \frac{1025831888427468187613336}{117649} a + \frac{1325970015560148997468622}{117649} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( 5 a^{5} - 49 a^{3} + 19 a^{2} + 101 a - 59\) , \( 2 a^{5} - 47 a^{4} + 97 a^{3} + 113 a^{2} - 290 a + 88\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-12a^{2}-a+6\right){x}^{2}+\left(5a^{5}-49a^{3}+19a^{2}+101a-59\right){x}+2a^{5}-47a^{4}+97a^{3}+113a^{2}-290a+88$ |
| 7.1-d5 |
7.1-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( 7^{4} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$2.022173880$ |
$61.21300997$ |
2.62611 |
\( -\frac{203442160742265836111311}{49} a^{5} + \frac{754939116457579934341120}{49} a^{4} - \frac{70918941964796608216091}{49} a^{3} - \frac{1913091408632068298504203}{49} a^{2} + \frac{1238551091877646917232536}{49} a + \frac{118914358788506027626050}{49} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -5 a^{5} + 61 a^{3} - 31 a^{2} - 139 a + 1\) , \( -44 a^{5} - 33 a^{4} + 383 a^{3} + 59 a^{2} - 696 a - 54\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-12a^{2}-a+6\right){x}^{2}+\left(-5a^{5}+61a^{3}-31a^{2}-139a+1\right){x}-44a^{5}-33a^{4}+383a^{3}+59a^{2}-696a-54$ |
| 7.1-d6 |
7.1-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$118.88391$ |
$(a^4-2a^3-3a^2+6a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$4.044347761$ |
$0.956453280$ |
2.62611 |
\( -\frac{1307780824025356872024765295948965037006665607}{7} a^{5} + \frac{4852951306689182093152206038520079788667830037}{7} a^{4} - 65126571056091535976357513219578497247532910 a^{3} - 1756837878700362061740707440950803215540288329 a^{2} + \frac{7961738912049866844077158263606893208018336752}{7} a + \frac{764413421276477386339801659357910076498899480}{7} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + a^{2} + 1\) , \( -a^{3} + 4 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -47 a^{5} - 2 a^{4} + 213 a^{3} + 36 a^{2} - 154 a - 15\) , \( -1023 a^{5} + 4977 a^{3} + 800 a^{2} - 4246 a + 90\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+a^{2}+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-47a^{5}-2a^{4}+213a^{3}+36a^{2}-154a-15\right){x}-1023a^{5}+4977a^{3}+800a^{2}-4246a+90$ |
| 7.2-a1 |
7.2-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( 7^{4} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$11015.21487$ |
1.21715 |
\( \frac{1791563}{49} a^{5} - \frac{2144001}{49} a^{4} - \frac{13353528}{49} a^{3} + \frac{7596885}{49} a^{2} + \frac{26935838}{49} a + \frac{2225112}{49} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 6 a^{2} - 2\) , \( -a^{4} + 5 a^{2} - 4\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 2 a\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 10 a + 3\) , \( a^{5} - 10 a^{4} + 9 a^{3} + 31 a^{2} - 32 a\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+6a^{2}-2\right){x}{y}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-2a\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-4\right){x}^{2}+\left(-a^{4}+3a^{3}+2a^{2}-10a+3\right){x}+a^{5}-10a^{4}+9a^{3}+31a^{2}-32a$ |
| 7.2-a2 |
7.2-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( 7^{8} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$2753.803719$ |
1.21715 |
\( \frac{6808447220731}{343} a^{5} - \frac{7293508831162}{343} a^{4} - \frac{47434801694810}{343} a^{3} + \frac{24264587042616}{343} a^{2} + \frac{89842625786419}{343} a + \frac{7427134913096}{343} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 2 a\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 3 a\) , \( a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 3 a\) , \( 22 a^{5} - 34 a^{4} - 68 a^{3} + 75 a^{2} + 2 a - 1\) , \( 7 a^{5} - 99 a^{4} + 109 a^{3} + 292 a^{2} - 260 a - 24\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-2a\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-3a\right){x}^{2}+\left(22a^{5}-34a^{4}-68a^{3}+75a^{2}+2a-1\right){x}+7a^{5}-99a^{4}+109a^{3}+292a^{2}-260a-24$ |
| 7.2-a3 |
7.2-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( 7^{16} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2 \) |
$1$ |
$43.02818311$ |
1.21715 |
\( \frac{112621865305044987921809}{117649} a^{5} + \frac{37380892926637841640926}{117649} a^{4} - \frac{588562124742511290364561}{117649} a^{3} - \frac{246258228057966485156651}{117649} a^{2} + \frac{551965382947279329722044}{117649} a + \frac{48295869496080970282609}{117649} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 6 a^{2} - 2\) , \( -a^{4} + 5 a^{2} - 4\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 2 a\) , \( -30 a^{5} + 104 a^{4} + 8 a^{3} - 288 a^{2} + 220 a - 67\) , \( -227 a^{5} + 789 a^{4} + 140 a^{3} - 2366 a^{2} + 1449 a + 19\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+6a^{2}-2\right){x}{y}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-2a\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-4\right){x}^{2}+\left(-30a^{5}+104a^{4}+8a^{3}-288a^{2}+220a-67\right){x}-227a^{5}+789a^{4}+140a^{3}-2366a^{2}+1449a+19$ |
| 7.2-a4 |
7.2-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$172.1127324$ |
1.21715 |
\( -\frac{559397469874345863}{7} a^{5} + \frac{1161037199594720055}{7} a^{4} + \frac{3276385318296976538}{7} a^{3} - \frac{5869137848808229957}{7} a^{2} - \frac{5153015175448576518}{7} a + \frac{6626604895369664957}{7} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 9 a^{2} + a + 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 7 a^{2} - 3\) , \( -2223 a^{5} - 477 a^{4} + 11253 a^{3} + 4047 a^{2} - 9888 a - 1188\) , \( 65543 a^{5} + 16241 a^{4} - 335030 a^{3} - 126044 a^{2} + 302842 a + 28386\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+7a^{2}-3\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-9a^{2}+a+2\right){x}^{2}+\left(-2223a^{5}-477a^{4}+11253a^{3}+4047a^{2}-9888a-1188\right){x}+65543a^{5}+16241a^{4}-335030a^{3}-126044a^{2}+302842a+28386$ |
| 7.2-a5 |
7.2-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( 7^{4} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2 \) |
$1$ |
$688.4509298$ |
1.21715 |
\( \frac{203442160742265836111311}{49} a^{5} - \frac{221977472264391486198942}{49} a^{4} - \frac{1422406400636662642993359}{49} a^{3} + \frac{741608530267585309002763}{49} a^{2} + \frac{2708463291733542388253636}{49} a + \frac{223835476847137903613375}{49} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + a - 1\) , \( a^{4} - 4 a^{2} - 2 a + 1\) , \( a^{5} - a^{4} - 3 a^{3} + a^{2} - a + 2\) , \( -123 a^{5} + 243 a^{4} + 367 a^{3} - 710 a^{2} + 8 a + 7\) , \( -110 a^{5} - 1977 a^{4} + 3245 a^{3} + 6620 a^{2} - 7432 a - 678\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+a-1\right){x}{y}+\left(a^{5}-a^{4}-3a^{3}+a^{2}-a+2\right){y}={x}^{3}+\left(a^{4}-4a^{2}-2a+1\right){x}^{2}+\left(-123a^{5}+243a^{4}+367a^{3}-710a^{2}+8a+7\right){x}-110a^{5}-1977a^{4}+3245a^{3}+6620a^{2}-7432a-678$ |
| 7.2-a6 |
7.2-a |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$256$ |
\( 2 \) |
$1$ |
$10.75704577$ |
1.21715 |
\( \frac{1307780824025356872024765295948965037006665607}{7} a^{5} - \frac{1426930782360125700490308291091787017129909047}{7} a^{4} - \frac{9143610193366820283442749807521617239815916698}{7} a^{3} + \frac{4767258720016713504152715749572825371641060421}{7} a^{2} + \frac{17410729135899459869092701189140814182089683462}{7} a + \frac{1438874534605637964988709222541326697190256371}{7} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a\) , \( a^{4} - 4 a^{2} - a + 1\) , \( 145 a^{5} - 16 a^{4} - 824 a^{3} - 170 a^{2} + 797 a - 38\) , \( -6563 a^{5} - 813 a^{4} + 37612 a^{3} + 13925 a^{2} - 35646 a - 2732\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+\left(a^{4}-4a^{2}-a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+3a\right){x}^{2}+\left(145a^{5}-16a^{4}-824a^{3}-170a^{2}+797a-38\right){x}-6563a^{5}-813a^{4}+37612a^{3}+13925a^{2}-35646a-2732$ |
| 7.2-b1 |
7.2-b |
$1$ |
$1$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{11} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$1912.003895$ |
1.69016 |
\( -\frac{149058165}{2401} a^{5} + \frac{356633036}{2401} a^{4} + \frac{699887273}{2401} a^{3} - \frac{1572783553}{2401} a^{2} - \frac{856194967}{2401} a + \frac{200729810}{343} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a + 1\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 6 a^{2} - 4 a - 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 7 a^{2} - a - 4\) , \( 4 a^{5} - 5 a^{4} - 15 a^{3} + 14 a^{2} + 10 a + 3\) , \( 2 a^{5} - 3 a^{4} - a^{3} + 11 a^{2} - 13 a - 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+7a^{2}-a-4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-2a^{3}+6a^{2}-4a-2\right){x}^{2}+\left(4a^{5}-5a^{4}-15a^{3}+14a^{2}+10a+3\right){x}+2a^{5}-3a^{4}-a^{3}+11a^{2}-13a-5$ |
| 7.2-c1 |
7.2-c |
$1$ |
$1$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{11} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 11 \) |
$0.008193862$ |
$4984.021577$ |
2.38261 |
\( -\frac{149058165}{2401} a^{5} + \frac{356633036}{2401} a^{4} + \frac{699887273}{2401} a^{3} - \frac{1572783553}{2401} a^{2} - \frac{856194967}{2401} a + \frac{200729810}{343} \) |
\( \bigl[a^{4} - 5 a^{2} - a + 3\) , \( a^{5} - a^{4} - 5 a^{3} + 2 a^{2} + 6 a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 7 a^{2} - 3\) , \( 5 a^{5} - 6 a^{4} - 39 a^{3} + 21 a^{2} + 83 a + 12\) , \( 5 a^{5} - 6 a^{4} - 37 a^{3} + 21 a^{2} + 74 a + 4\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}-a+3\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+7a^{2}-3\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+2a^{2}+6a\right){x}^{2}+\left(5a^{5}-6a^{4}-39a^{3}+21a^{2}+83a+12\right){x}+5a^{5}-6a^{4}-37a^{3}+21a^{2}+74a+4$ |
| 7.2-d1 |
7.2-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( 7^{4} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
$0 \le r \le 5$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2^{2} \) |
$1$ |
$15670.53055$ |
2.62611 |
\( \frac{1791563}{49} a^{5} - \frac{2144001}{49} a^{4} - \frac{13353528}{49} a^{3} + \frac{7596885}{49} a^{2} + \frac{26935838}{49} a + \frac{2225112}{49} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 2 a - 5\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 13 a^{5} - 5 a^{4} - 54 a^{3} + 27 a + 11\) , \( 30 a^{5} - a^{4} - 145 a^{3} - 27 a^{2} + 119 a + 5\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+8a^{2}+2a-5\right){x}^{2}+\left(13a^{5}-5a^{4}-54a^{3}+27a+11\right){x}+30a^{5}-a^{4}-145a^{3}-27a^{2}+119a+5$ |
| 7.2-d2 |
7.2-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( 7^{8} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
$0 \le r \le 5$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
|
\( 2^{3} \) |
$1$ |
$3917.632638$ |
2.62611 |
\( \frac{6808447220731}{343} a^{5} - \frac{7293508831162}{343} a^{4} - \frac{47434801694810}{343} a^{3} + \frac{24264587042616}{343} a^{2} + \frac{89842625786419}{343} a + \frac{7427134913096}{343} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 2 a - 5\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 13 a^{5} - 5 a^{4} - 54 a^{3} + 27 a + 6\) , \( 26 a^{5} + 2 a^{4} - 126 a^{3} - 37 a^{2} + 105 a + 8\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+8a^{2}+2a-5\right){x}^{2}+\left(13a^{5}-5a^{4}-54a^{3}+27a+6\right){x}+26a^{5}+2a^{4}-126a^{3}-37a^{2}+105a+8$ |
| 7.2-d3 |
7.2-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( 7^{16} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
$0 \le r \le 5$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2^{4} \) |
$1$ |
$979.4081595$ |
2.62611 |
\( \frac{112621865305044987921809}{117649} a^{5} + \frac{37380892926637841640926}{117649} a^{4} - \frac{588562124742511290364561}{117649} a^{3} - \frac{246258228057966485156651}{117649} a^{2} + \frac{551965382947279329722044}{117649} a + \frac{48295869496080970282609}{117649} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 2 a - 5\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 8 a^{5} + 5 a^{4} - 49 a^{3} - 25 a^{2} + 47 a + 1\) , \( -10 a^{5} + 68 a^{3} + 8 a^{2} - 80 a + 17\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+8a^{2}+2a-5\right){x}^{2}+\left(8a^{5}+5a^{4}-49a^{3}-25a^{2}+47a+1\right){x}-10a^{5}+68a^{3}+8a^{2}-80a+17$ |
| 7.2-d4 |
7.2-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
$0 \le r \le 5$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$0.956453280$ |
2.62611 |
\( -\frac{559397469874345863}{7} a^{5} + \frac{1161037199594720055}{7} a^{4} + \frac{3276385318296976538}{7} a^{3} - \frac{5869137848808229957}{7} a^{2} - \frac{5153015175448576518}{7} a + \frac{6626604895369664957}{7} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 2592 a^{5} - 5528 a^{4} - 14757 a^{3} + 27298 a^{2} + 22839 a - 30094\) , \( 174845 a^{5} - 365827 a^{4} - 1014404 a^{3} + 1835698 a^{2} + 1583981 a - 2053308\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-2a-2\right){x}^{2}+\left(2592a^{5}-5528a^{4}-14757a^{3}+27298a^{2}+22839a-30094\right){x}+174845a^{5}-365827a^{4}-1014404a^{3}+1835698a^{2}+1583981a-2053308$ |
| 7.2-d5 |
7.2-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( 7^{4} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
$0 \le r \le 5$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
|
\( 2^{2} \) |
$1$ |
$61.21300997$ |
2.62611 |
\( \frac{203442160742265836111311}{49} a^{5} - \frac{221977472264391486198942}{49} a^{4} - \frac{1422406400636662642993359}{49} a^{3} + \frac{741608530267585309002763}{49} a^{2} + \frac{2708463291733542388253636}{49} a + \frac{223835476847137903613375}{49} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 8 a^{2} + 2 a - 5\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 18 a^{5} - 15 a^{4} - 59 a^{3} + 25 a^{2} + 7 a - 69\) , \( 26 a^{5} - 4 a^{4} - 44 a^{3} - 102 a^{2} - 46 a - 149\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+8a^{2}+2a-5\right){x}^{2}+\left(18a^{5}-15a^{4}-59a^{3}+25a^{2}+7a-69\right){x}+26a^{5}-4a^{4}-44a^{3}-102a^{2}-46a-149$ |
| 7.2-d6 |
7.2-d |
$6$ |
$8$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$118.88391$ |
$(-a^4+a^3+4a^2-a-1)$ |
$0 \le r \le 5$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
|
\( 2 \) |
$1$ |
$0.956453280$ |
2.62611 |
\( \frac{1307780824025356872024765295948965037006665607}{7} a^{5} - \frac{1426930782360125700490308291091787017129909047}{7} a^{4} - \frac{9143610193366820283442749807521617239815916698}{7} a^{3} + \frac{4767258720016713504152715749572825371641060421}{7} a^{2} + \frac{17410729135899459869092701189140814182089683462}{7} a + \frac{1438874534605637964988709222541326697190256371}{7} \) |
\( \bigl[a^{5} - 2 a^{4} - 2 a^{3} + 5 a^{2} - 2 a - 1\) , \( -a^{5} + a^{4} + 3 a^{3} - a^{2} + a - 2\) , \( a\) , \( 48 a^{5} - 57 a^{4} - 384 a^{3} + 429 a^{2} + 713 a - 758\) , \( 724 a^{5} - 1072 a^{4} - 4688 a^{3} + 5920 a^{2} + 7542 a - 8105\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-2a^{3}+5a^{2}-2a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{5}+a^{4}+3a^{3}-a^{2}+a-2\right){x}^{2}+\left(48a^{5}-57a^{4}-384a^{3}+429a^{2}+713a-758\right){x}+724a^{5}-1072a^{4}-4688a^{3}+5920a^{2}+7542a-8105$ |
| 13.1-a1 |
13.1-a |
$2$ |
$2$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13^{4} \) |
$125.17767$ |
$(a^5+a^4-6a^3-5a^2+7a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.022707472$ |
$25153.71661$ |
3.02944 |
\( \frac{3142535}{169} a^{4} - \frac{8706695}{169} a^{3} - \frac{7005980}{169} a^{2} + \frac{22977550}{169} a + \frac{2288096}{169} \) |
\( \bigl[a + 1\) , \( -a^{4} + 5 a^{2} - 4\) , \( a^{4} - 4 a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - 3 a + 4\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 7 a - 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{4}-4a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}+5a^{2}-4\right){x}^{2}+\left(a^{3}-a^{2}-3a+4\right){x}-a^{5}-a^{4}+6a^{3}+5a^{2}-7a-3$ |
| 13.1-a2 |
13.1-a |
$2$ |
$2$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13^{8} \) |
$125.17767$ |
$(a^5+a^4-6a^3-5a^2+7a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.011353736$ |
$25153.71661$ |
3.02944 |
\( \frac{40011414891545}{28561} a^{4} - \frac{112109526044994}{28561} a^{3} - \frac{87947548412731}{28561} a^{2} + \frac{296317163243437}{28561} a + \frac{25731563801416}{28561} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 6 a^{2} - 2\) , \( -1\) , \( 0\) , \( -24 a^{5} - 4 a^{4} + 120 a^{3} + 40 a^{2} - 104 a - 12\) , \( -12 a^{5} + 3 a^{4} + 54 a^{3} + 3 a^{2} - 37 a - 3\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+6a^{2}-2\right){x}{y}={x}^{3}-{x}^{2}+\left(-24a^{5}-4a^{4}+120a^{3}+40a^{2}-104a-12\right){x}-12a^{5}+3a^{4}+54a^{3}+3a^{2}-37a-3$ |
| 13.1-b1 |
13.1-b |
$2$ |
$2$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13^{4} \) |
$125.17767$ |
$(a^5+a^4-6a^3-5a^2+7a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.022707472$ |
$25153.71661$ |
3.02944 |
\( \frac{3142535}{169} a^{4} - \frac{8706695}{169} a^{3} - \frac{7005980}{169} a^{2} + \frac{22977550}{169} a + \frac{2288096}{169} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 2\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + a - 2\) , \( -a^{5} - a^{4} + 8 a^{3} + 2 a^{2} - 13 a + 8\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 7 a^{2} + 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+a-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+2\right){x}^{2}+\left(-a^{5}-a^{4}+8a^{3}+2a^{2}-13a+8\right){x}-a^{5}+2a^{4}+3a^{3}-7a^{2}+3$ |
| 13.1-b2 |
13.1-b |
$2$ |
$2$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( 13^{8} \) |
$125.17767$ |
$(a^5+a^4-6a^3-5a^2+7a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.011353736$ |
$25153.71661$ |
3.02944 |
\( \frac{40011414891545}{28561} a^{4} - \frac{112109526044994}{28561} a^{3} - \frac{87947548412731}{28561} a^{2} + \frac{296317163243437}{28561} a + \frac{25731563801416}{28561} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + a^{2} - a + 2\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 11 a^{2} + 2 a + 5\) , \( a^{3} - 4 a\) , \( 23 a^{5} - 47 a^{4} - 133 a^{3} + 234 a^{2} + 204 a - 262\) , \( 51 a^{5} - 106 a^{4} - 298 a^{3} + 535 a^{2} + 467 a - 604\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+a^{2}-a+2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-11a^{2}+2a+5\right){x}^{2}+\left(23a^{5}-47a^{4}-133a^{3}+234a^{2}+204a-262\right){x}+51a^{5}-106a^{4}-298a^{3}+535a^{2}+467a-604$ |
| 29.3-a1 |
29.3-a |
$1$ |
$1$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{3} \) |
$133.83347$ |
$(a^4-a^3-3a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.002830732$ |
$70594.46889$ |
3.17967 |
\( -\frac{86278465922}{24389} a^{5} - \frac{47189236829}{24389} a^{4} + \frac{438778368281}{24389} a^{3} + \frac{277275142138}{24389} a^{2} - \frac{358957259814}{24389} a - \frac{88742923489}{24389} \) |
\( \bigl[a^{5} - 2 a^{4} - 2 a^{3} + 5 a^{2} - 2 a - 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{4} - 5 a^{2} + 4\) , \( a^{5} + 4 a^{4} - 7 a^{3} - 16 a^{2} + 7 a + 4\) , \( 4 a^{5} + 2 a^{4} - 24 a^{3} - 9 a^{2} + 29 a - 1\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-2a^{3}+5a^{2}-2a-1\right){x}{y}+\left(a^{4}-5a^{2}+4\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+2\right){x}^{2}+\left(a^{5}+4a^{4}-7a^{3}-16a^{2}+7a+4\right){x}+4a^{5}+2a^{4}-24a^{3}-9a^{2}+29a-1$ |
| 29.3-b1 |
29.3-b |
$2$ |
$5$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{5} \) |
$133.83347$ |
$(a^4-a^3-3a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$0.072380082$ |
$1279.479688$ |
2.45592 |
\( -\frac{34286919698837807988428}{20511149} a^{5} - \frac{11384698874034008601269}{20511149} a^{4} + \frac{179179369561896340242986}{20511149} a^{3} + \frac{74989014479850097421206}{20511149} a^{2} - \frac{168020705700556465895183}{20511149} a - \frac{14701659055200981175163}{20511149} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 4 a^{2} - a + 2\) , \( a^{2} - a - 2\) , \( 78 a^{5} - 344 a^{4} + 69 a^{3} + 933 a^{2} - 534 a - 149\) , \( 889 a^{5} - 3638 a^{4} + 2347 a^{3} + 7042 a^{2} - 10634 a + 4016\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-2a^{3}+4a^{2}-a+2\right){x}^{2}+\left(78a^{5}-344a^{4}+69a^{3}+933a^{2}-534a-149\right){x}+889a^{5}-3638a^{4}+2347a^{3}+7042a^{2}-10634a+4016$ |
| 29.3-b2 |
29.3-b |
$2$ |
$5$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$133.83347$ |
$(a^4-a^3-3a^2+a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.014476016$ |
$31986.99220$ |
2.45592 |
\( \frac{23970}{29} a^{5} - \frac{73281}{29} a^{4} - \frac{77587}{29} a^{3} + \frac{268660}{29} a^{2} + \frac{49483}{29} a - \frac{112985}{29} \) |
\( \bigl[a^{5} - 2 a^{4} - 2 a^{3} + 6 a^{2} - 4 a - 3\) , \( -a^{5} + a^{4} + 5 a^{3} - 2 a^{2} - 5 a - 2\) , \( 0\) , \( -2 a^{5} + 2 a^{4} + 15 a^{3} - 6 a^{2} - 29 a - 3\) , \( 2 a^{5} - 2 a^{4} - 14 a^{3} + 7 a^{2} + 27 a + 2\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-2a^{3}+6a^{2}-4a-3\right){x}{y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-2a^{2}-5a-2\right){x}^{2}+\left(-2a^{5}+2a^{4}+15a^{3}-6a^{2}-29a-3\right){x}+2a^{5}-2a^{4}-14a^{3}+7a^{2}+27a+2$ |
| 29.3-c1 |
29.3-c |
$2$ |
$5$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{5} \) |
$133.83347$ |
$(a^4-a^3-3a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$3.987160790$ |
2.20285 |
\( -\frac{34286919698837807988428}{20511149} a^{5} - \frac{11384698874034008601269}{20511149} a^{4} + \frac{179179369561896340242986}{20511149} a^{3} + \frac{74989014479850097421206}{20511149} a^{2} - \frac{168020705700556465895183}{20511149} a - \frac{14701659055200981175163}{20511149} \) |
\( \bigl[a^{2} - 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 2\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 6 a^{2} - 3 a - 2\) , \( 65 a^{5} - 151 a^{4} - 347 a^{3} + 706 a^{2} + 535 a - 744\) , \( 8693 a^{5} - 18199 a^{4} - 50436 a^{3} + 91318 a^{2} + 78787 a - 102152\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{5}-2a^{4}-2a^{3}+6a^{2}-3a-2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-2\right){x}^{2}+\left(65a^{5}-151a^{4}-347a^{3}+706a^{2}+535a-744\right){x}+8693a^{5}-18199a^{4}-50436a^{3}+91318a^{2}+78787a-102152$ |
| 29.3-c2 |
29.3-c |
$2$ |
$5$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29 \) |
$133.83347$ |
$(a^4-a^3-3a^2+a-2)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$62299.38735$ |
2.20285 |
\( \frac{23970}{29} a^{5} - \frac{73281}{29} a^{4} - \frac{77587}{29} a^{3} + \frac{268660}{29} a^{2} + \frac{49483}{29} a - \frac{112985}{29} \) |
\( \bigl[a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a\) , \( a^{3} - 3 a\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 2 a^{2} + 14 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{5}-a^{4}-5a^{3}+3a^{2}+6a\right){x}^{2}+\left(2a^{5}-a^{4}-11a^{3}+2a^{2}+14a+1\right){x}$ |
| 29.3-d1 |
29.3-d |
$1$ |
$1$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.3 |
\( 29 \) |
\( 29^{3} \) |
$133.83347$ |
$(a^4-a^3-3a^2+a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$1581.476661$ |
1.39799 |
\( -\frac{86278465922}{24389} a^{5} - \frac{47189236829}{24389} a^{4} + \frac{438778368281}{24389} a^{3} + \frac{277275142138}{24389} a^{2} - \frac{358957259814}{24389} a - \frac{88742923489}{24389} \) |
\( \bigl[a^{5} - a^{4} - 4 a^{3} + 2 a^{2} + 2 a\) , \( -a^{5} + a^{4} + 3 a^{3} - 2 a^{2} + 3 a\) , \( a^{5} - a^{4} - 3 a^{3} + a^{2} - a + 2\) , \( -a^{5} - 2 a^{4} + 5 a^{3} + 12 a^{2} - 3 a - 7\) , \( -a^{4} - a^{3} + 5 a^{2} + 5 a - 7\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-4a^{3}+2a^{2}+2a\right){x}{y}+\left(a^{5}-a^{4}-3a^{3}+a^{2}-a+2\right){y}={x}^{3}+\left(-a^{5}+a^{4}+3a^{3}-2a^{2}+3a\right){x}^{2}+\left(-a^{5}-2a^{4}+5a^{3}+12a^{2}-3a-7\right){x}-a^{4}-a^{3}+5a^{2}+5a-7$ |
| 29.4-a1 |
29.4-a |
$1$ |
$1$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{3} \) |
$133.83347$ |
$(a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 3 \) |
$0.002830732$ |
$70594.46889$ |
3.17967 |
\( \frac{86278465922}{24389} a^{5} - \frac{182182699415}{24389} a^{4} - \frac{538007746397}{24389} a^{3} + \frac{968813917198}{24389} a^{2} + \frac{886017330406}{24389} a - \frac{1130815496961}{24389} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + a^{2} + 1\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 7 a^{2} + 3\) , \( a^{4} - a^{3} - 3 a^{2} + a + 1\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 5 a^{2} + 13 a - 6\) , \( a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 5 a + 3\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+a^{2}+1\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+a+1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-7a^{2}+3\right){x}^{2}+\left(2a^{5}-a^{4}-12a^{3}+5a^{2}+13a-6\right){x}+a^{5}+a^{4}-5a^{3}-6a^{2}+5a+3$ |
| 29.4-b1 |
29.4-b |
$2$ |
$5$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{5} \) |
$133.83347$ |
$(a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 5 \) |
$0.072380082$ |
$1279.479688$ |
2.45592 |
\( \frac{34286919698837807988428}{20511149} a^{5} - \frac{71481909750259171305404}{20511149} a^{4} - \frac{199666497045499987826938}{20511149} a^{3} + \frac{359831156125219449696111}{20511149} a^{2} + \frac{312348696775660588553712}{20511149} a - \frac{403713904104228202715024}{20511149} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 11 a^{2} + 2 a + 7\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -239 a^{5} + 334 a^{4} + 1490 a^{3} - 1095 a^{2} - 2633 a - 202\) , \( -5267 a^{5} + 5231 a^{4} + 38172 a^{3} - 17686 a^{2} - 74263 a - 6150\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-11a^{2}+2a+7\right){x}^{2}+\left(-239a^{5}+334a^{4}+1490a^{3}-1095a^{2}-2633a-202\right){x}-5267a^{5}+5231a^{4}+38172a^{3}-17686a^{2}-74263a-6150$ |
| 29.4-b2 |
29.4-b |
$2$ |
$5$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29 \) |
$133.83347$ |
$(a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$0.014476016$ |
$31986.99220$ |
2.45592 |
\( -\frac{23970}{29} a^{5} + \frac{6171}{29} a^{4} + \frac{106200}{29} a^{3} + \frac{38277}{29} a^{2} - \frac{68212}{29} a - \frac{40593}{29} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 7 a^{2} - a - 4\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 5 a + 1\) , \( 0\) , \( 2 a^{5} - 9 a^{4} + 5 a^{3} + 21 a^{2} - 24 a + 6\) , \( -2 a^{5} + 7 a^{4} + a^{3} - 19 a^{2} + 7 a + 5\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+7a^{2}-a-4\right){x}{y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-3a^{2}-5a+1\right){x}^{2}+\left(2a^{5}-9a^{4}+5a^{3}+21a^{2}-24a+6\right){x}-2a^{5}+7a^{4}+a^{3}-19a^{2}+7a+5$ |
| 29.4-c1 |
29.4-c |
$2$ |
$5$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{5} \) |
$133.83347$ |
$(a^2-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$625$ |
\( 1 \) |
$1$ |
$3.987160790$ |
2.20285 |
\( \frac{34286919698837807988428}{20511149} a^{5} - \frac{71481909750259171305404}{20511149} a^{4} - \frac{199666497045499987826938}{20511149} a^{3} + \frac{359831156125219449696111}{20511149} a^{2} + \frac{312348696775660588553712}{20511149} a - \frac{403713904104228202715024}{20511149} \) |
\( \bigl[a^{4} - 5 a^{2} + 3\) , \( -a^{5} + a^{4} + 5 a^{3} - 2 a^{2} - 5 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 1\) , \( 19 a^{5} + 33 a^{4} - 88 a^{3} - 192 a^{2} - 69 a - 4\) , \( 176 a^{5} + 209 a^{4} - 870 a^{3} - 1383 a^{2} - 286 a - 16\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+3\right){x}{y}+\left(a^{5}-a^{4}-4a^{3}+3a^{2}+2a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-2a^{2}-5a-2\right){x}^{2}+\left(19a^{5}+33a^{4}-88a^{3}-192a^{2}-69a-4\right){x}+176a^{5}+209a^{4}-870a^{3}-1383a^{2}-286a-16$ |
| 29.4-c2 |
29.4-c |
$2$ |
$5$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29 \) |
$133.83347$ |
$(a^2-a-1)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$62299.38735$ |
2.20285 |
\( -\frac{23970}{29} a^{5} + \frac{6171}{29} a^{4} + \frac{106200}{29} a^{3} + \frac{38277}{29} a^{2} - \frac{68212}{29} a - \frac{40593}{29} \) |
\( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( -a^{5} + a^{4} + 3 a^{3} - 2 a^{2} + 3 a + 2\) , \( a\) , \( -4 a^{4} + 2 a^{3} + 16 a^{2} + 2 a - 3\) , \( -2 a^{4} - a^{3} + 11 a^{2} + 8 a - 8\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{5}+a^{4}+3a^{3}-2a^{2}+3a+2\right){x}^{2}+\left(-4a^{4}+2a^{3}+16a^{2}+2a-3\right){x}-2a^{4}-a^{3}+11a^{2}+8a-8$ |
| 29.4-d1 |
29.4-d |
$1$ |
$1$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
29.4 |
\( 29 \) |
\( 29^{3} \) |
$133.83347$ |
$(a^2-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3Ns |
$1$ |
\( 1 \) |
$1$ |
$1581.476661$ |
1.39799 |
\( \frac{86278465922}{24389} a^{5} - \frac{182182699415}{24389} a^{4} - \frac{538007746397}{24389} a^{3} + \frac{968813917198}{24389} a^{2} + \frac{886017330406}{24389} a - \frac{1130815496961}{24389} \) |
\( \bigl[a^{5} - 2 a^{4} - 2 a^{3} + 5 a^{2} - 3 a\) , \( a - 1\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 5 a^{2} - 3 a - 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 1\) , \( -2 a^{5} + 3 a^{4} + 6 a^{3} - 8 a^{2} + a\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-2a^{3}+5a^{2}-3a\right){x}{y}+\left(a^{5}-2a^{4}-2a^{3}+5a^{2}-3a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{4}-2a^{3}-4a^{2}+7a+1\right){x}-2a^{5}+3a^{4}+6a^{3}-8a^{2}+a$ |
| 41.1-a1 |
41.1-a |
$4$ |
$10$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{20} \) |
$137.75168$ |
$(a^5-2a^4-3a^3+6a^2-4)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
|
\( 2^{2} \cdot 5 \) |
$1$ |
$28.02091986$ |
4.00367 |
\( -\frac{357571850055303381213985}{13422659310152401} a^{4} + \frac{540487576413107354164635}{13422659310152401} a^{3} + \frac{1247371673863409551905290}{13422659310152401} a^{2} - \frac{1263890879184018681279920}{13422659310152401} a - \frac{115913951592431810832436}{13422659310152401} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - a\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 3 a\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - a\) , \( 607 a^{5} - 963 a^{4} - 3035 a^{3} + 3862 a^{2} + 3594 a - 4032\) , \( -9346 a^{5} + 11784 a^{4} + 60096 a^{3} - 63006 a^{2} - 89033 a + 85118\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-a\right){x}{y}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-a\right){y}={x}^{3}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-3a\right){x}^{2}+\left(607a^{5}-963a^{4}-3035a^{3}+3862a^{2}+3594a-4032\right){x}-9346a^{5}+11784a^{4}+60096a^{3}-63006a^{2}-89033a+85118$ |
| 41.1-a2 |
41.1-a |
$4$ |
$10$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$137.75168$ |
$(a^5-2a^4-3a^3+6a^2-4)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
|
\( 2 \) |
$1$ |
$2802.091986$ |
4.00367 |
\( -\frac{734681}{41} a^{4} - \frac{233799}{41} a^{3} + \frac{3907204}{41} a^{2} + \frac{1436078}{41} a - \frac{3784992}{41} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( a^{2} - a - 1\) , \( a^{5} + 4 a^{4} - 9 a^{3} - 12 a^{2} + 11 a - 4\) , \( 2 a^{5} + 5 a^{4} - 18 a^{3} - 15 a^{2} + 28 a - 5\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+a+1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){x}^{2}+\left(a^{5}+4a^{4}-9a^{3}-12a^{2}+11a-4\right){x}+2a^{5}+5a^{4}-18a^{3}-15a^{2}+28a-5$ |
| 41.1-a3 |
41.1-a |
$4$ |
$10$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{4} \) |
$137.75168$ |
$(a^5-2a^4-3a^3+6a^2-4)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
|
\( 2^{2} \) |
$1$ |
$700.5229965$ |
4.00367 |
\( \frac{2962060985575}{1681} a^{4} + \frac{731644682050}{1681} a^{3} - \frac{15541949609925}{1681} a^{2} - \frac{5156995031725}{1681} a + \frac{14955417009784}{1681} \) |
\( \bigl[a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - a\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 3 a\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - a\) , \( 117 a^{5} - 193 a^{4} - 665 a^{3} + 952 a^{2} + 959 a - 1097\) , \( 1324 a^{5} - 2576 a^{4} - 7659 a^{3} + 12919 a^{2} + 11717 a - 14637\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-a\right){x}{y}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-a\right){y}={x}^{3}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-3a\right){x}^{2}+\left(117a^{5}-193a^{4}-665a^{3}+952a^{2}+959a-1097\right){x}+1324a^{5}-2576a^{4}-7659a^{3}+12919a^{2}+11717a-14637$ |
| 41.1-a4 |
41.1-a |
$4$ |
$10$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{10} \) |
$137.75168$ |
$(a^5-2a^4-3a^3+6a^2-4)$ |
$0 \le r \le 1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
|
\( 2 \cdot 5 \) |
$1$ |
$112.0836794$ |
4.00367 |
\( \frac{815501597212588028076}{115856201} a^{4} - \frac{2284984698342134580907}{115856201} a^{3} - \frac{1792523287720805559473}{115856201} a^{2} + \frac{6039452497813815714645}{115856201} a + \frac{524452446825637320235}{115856201} \) |
\( \bigl[a^{4} - 4 a^{2} - a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{5} - a^{4} - 3 a^{3} + 2 a^{2} - 2 a\) , \( 92 a^{5} - 24 a^{4} - 448 a^{3} - 78 a^{2} + 360 a + 40\) , \( 204 a^{5} + a^{4} - 584 a^{3} + 13 a^{2} + 285 a + 44\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}-a+1\right){x}{y}+\left(a^{5}-a^{4}-3a^{3}+2a^{2}-2a\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+3\right){x}^{2}+\left(92a^{5}-24a^{4}-448a^{3}-78a^{2}+360a+40\right){x}+204a^{5}+a^{4}-584a^{3}+13a^{2}+285a+44$ |
| 41.1-b1 |
41.1-b |
$4$ |
$10$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{20} \) |
$137.75168$ |
$(a^5-2a^4-3a^3+6a^2-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{2} \cdot 5 \) |
$2.280632233$ |
$1.843695156$ |
2.78770 |
\( -\frac{357571850055303381213985}{13422659310152401} a^{4} + \frac{540487576413107354164635}{13422659310152401} a^{3} + \frac{1247371673863409551905290}{13422659310152401} a^{2} - \frac{1263890879184018681279920}{13422659310152401} a - \frac{115913951592431810832436}{13422659310152401} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 3 a\) , \( 1\) , \( -10 a^{4} + 109 a^{3} - 59 a^{2} - 317 a - 71\) , \( -216 a^{4} + 1168 a^{3} - 88 a^{2} - 3288 a - 374\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-10a^{4}+109a^{3}-59a^{2}-317a-71\right){x}-216a^{4}+1168a^{3}-88a^{2}-3288a-374$ |
| 41.1-b2 |
41.1-b |
$4$ |
$10$ |
6.6.1279733.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$137.75168$ |
$(a^5-2a^4-3a^3+6a^2-4)$ |
$1$ |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \) |
$0.228063223$ |
$115230.9472$ |
2.78770 |
\( -\frac{734681}{41} a^{4} - \frac{233799}{41} a^{3} + \frac{3907204}{41} a^{2} + \frac{1436078}{41} a - \frac{3784992}{41} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 3 a\) , \( 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+3a\right){x}^{2}+\left(-a^{3}+a^{2}+3a-1\right){x}$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
