| 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 |
| 8.1-a1 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{42} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.6.3 |
$1$ |
\( 2 \) |
$1$ |
$13029.94564$ |
2.57985 |
\( -\frac{189613868625}{128} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{4} + 6 a^{2} - 6\) , \( a^{5} - 4 a^{3} + 2 a\) , \( a^{4} - 5 a^{2} - 115\) , \( 40 a^{4} - 240 a^{2} + 713\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{5}-4a^{3}+2a\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-6\right){x}^{2}+\left(a^{4}-5a^{2}-115\right){x}+40a^{4}-240a^{2}+713$ |
| 8.1-a2 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.6.1 |
$9$ |
\( 2 \) |
$1$ |
$160.8635265$ |
2.57985 |
\( -\frac{140625}{8} \) |
\( \bigl[a\) , \( a^{4} - 6 a^{2} + 6\) , \( a^{5} - 5 a^{3} + 4 a\) , \( -3 a^{2} + 5\) , \( -2 a^{2} + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-5a^{3}+4a\right){y}={x}^{3}+\left(a^{4}-6a^{2}+6\right){x}^{2}+\left(-3a^{2}+5\right){x}-2a^{2}+2$ |
| 8.1-a3 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{126} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.6.3 |
$9$ |
\( 2 \) |
$1$ |
$160.8635265$ |
2.57985 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[a\) , \( a^{4} - 6 a^{2} + 6\) , \( a^{5} - 5 a^{3} + 4 a\) , \( -10 a^{4} - 3 a^{2} + 5\) , \( 166 a^{4} - 246 a^{2} + 80\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-5a^{3}+4a\right){y}={x}^{3}+\left(a^{4}-6a^{2}+6\right){x}^{2}+\left(-10a^{4}-3a^{2}+5\right){x}+166a^{4}-246a^{2}+80$ |
| 8.1-a4 |
8.1-a |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.6.1 |
$1$ |
\( 2 \) |
$1$ |
$13029.94564$ |
2.57985 |
\( \frac{3375}{2} \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{4} + 6 a^{2} - 6\) , \( a^{5} - 4 a^{3} + 2 a\) , \( a^{4} - 5 a^{2} + 5\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{5}-4a^{3}+2a\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-6\right){x}^{2}+\left(a^{4}-5a^{2}+5\right){x}-1$ |
| 8.1-b1 |
8.1-b |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{42} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.1.3 |
$49$ |
\( 2 \cdot 7 \) |
$3.080173468$ |
$0.141300615$ |
1.59609 |
\( -\frac{189613868625}{128} \) |
\( \bigl[1\) , \( a^{4} - 6 a^{2} + 5\) , \( a^{4} - 4 a^{2} + 3\) , \( -118\) , \( -40 a^{4} + 239 a^{2} - 713\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(a^{4}-6a^{2}+5\right){x}^{2}-118{x}-40a^{4}+239a^{2}-713$ |
| 8.1-b2 |
8.1-b |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
$1$ |
$\Z/21\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.146674927$ |
$149614.8855$ |
1.59609 |
\( -\frac{140625}{8} \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{4} + 6 a^{2} - 7\) , \( a^{2} - 2\) , \( a^{4} - 8 a^{2} + 9\) , \( 2 a^{2} - 3\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-7\right){x}^{2}+\left(a^{4}-8a^{2}+9\right){x}+2a^{2}-3$ |
| 8.1-b3 |
8.1-b |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{126} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.1, 7B.1.3 |
$49$ |
\( 2 \cdot 3 \cdot 7 \) |
$1.026724489$ |
$1.271705543$ |
1.59609 |
\( -\frac{1159088625}{2097152} \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{4} + 6 a^{2} - 7\) , \( a^{2} - 2\) , \( -9 a^{4} - 8 a^{2} + 9\) , \( -166 a^{4} + 246 a^{2} - 81\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+6a^{2}-7\right){x}^{2}+\left(-9a^{4}-8a^{2}+9\right){x}-166a^{4}+246a^{2}-81$ |
| 8.1-b4 |
8.1-b |
$4$ |
$21$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$119.27013$ |
$(-a^4-a^3+3a^2+2a-1)$ |
$1$ |
$\Z/7\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 7$ |
3B.1.2, 7B.1.1 |
$1$ |
\( 2 \) |
$0.440024781$ |
$16623.87616$ |
1.59609 |
\( \frac{3375}{2} \) |
\( \bigl[1\) , \( a^{4} - 6 a^{2} + 5\) , \( a^{4} - 4 a^{2} + 3\) , \( 2\) , \( -a^{2} + 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(a^{4}-6a^{2}+5\right){x}^{2}+2{x}-a^{2}+1$ |
| 9.1-a1 |
9.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$120.44656$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$25806.98966$ |
1.27741 |
\( 1728 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 3 a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}$ |
| 9.1-a2 |
9.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$120.44656$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$1$ |
$25806.98966$ |
1.27741 |
\( 1728 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( a^{3} - 3 a - 1\) , \( 1\) , \( -a^{3} + 3 a + 1\) , \( -1\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(-a^{3}+3a+1\right){x}-1$ |
| 9.1-a3 |
9.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$120.44656$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$318.6048106$ |
1.27741 |
\( 44330496 a^{3} - 132991488 a + 76771008 \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 7 a + 5\) , \( a^{4} - 4 a^{2} + 3\) , \( 28 a^{5} - 18 a^{4} - 159 a^{3} + 94 a^{2} + 187 a - 108\) , \( 132 a^{5} - 94 a^{4} - 737 a^{3} + 507 a^{2} + 858 a - 582\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+7a+5\right){x}^{2}+\left(28a^{5}-18a^{4}-159a^{3}+94a^{2}+187a-108\right){x}+132a^{5}-94a^{4}-737a^{3}+507a^{2}+858a-582$ |
| 9.1-a4 |
9.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$120.44656$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/18\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$232262.9069$ |
1.27741 |
\( 44330496 a^{3} - 132991488 a + 76771008 \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 8 a - 4\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( 27 a^{5} - 19 a^{4} - 152 a^{3} + 99 a^{2} + 176 a - 113\) , \( -104 a^{5} + 75 a^{4} + 579 a^{3} - 408 a^{2} - 674 a + 468\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+5a^{2}-8a-4\right){x}^{2}+\left(27a^{5}-19a^{4}-152a^{3}+99a^{2}+176a-113\right){x}-104a^{5}+75a^{4}+579a^{3}-408a^{2}-674a+468$ |
| 9.1-a5 |
9.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$120.44656$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/18\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$232262.9069$ |
1.27741 |
\( -44330496 a^{3} + 132991488 a + 76771008 \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 18 a^{5} + 25 a^{4} - 73 a^{3} - 105 a^{2} + 12 a + 31\) , \( -81 a^{5} - 108 a^{4} + 346 a^{3} + 465 a^{2} - 124 a - 180\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4a+2\right){x}^{2}+\left(18a^{5}+25a^{4}-73a^{3}-105a^{2}+12a+31\right){x}-81a^{5}-108a^{4}+346a^{3}+465a^{2}-124a-180$ |
| 9.1-a6 |
9.1-a |
$6$ |
$18$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$120.44656$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$318.6048106$ |
1.27741 |
\( -44330496 a^{3} + 132991488 a + 76771008 \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + a - 1\) , \( a^{2} - 1\) , \( 19 a^{5} + 22 a^{4} - 76 a^{3} - 93 a^{2} + 10 a + 26\) , \( 99 a^{5} + 131 a^{4} - 418 a^{3} - 562 a^{2} + 132 a + 206\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{5}-a^{4}-4a^{3}+4a^{2}+a-1\right){x}^{2}+\left(19a^{5}+22a^{4}-76a^{3}-93a^{2}+10a+26\right){x}+99a^{5}+131a^{4}-418a^{3}-562a^{2}+132a+206$ |
| 27.1-a1 |
27.1-a |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1929.648952$ |
1.71926 |
\( -818991 a^{5} + 1040202 a^{4} + 3564270 a^{3} - 4511700 a^{2} - 1504170 a + 1853631 \) |
\( \bigl[a^{5} - 5 a^{3} + 5 a\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 3\) , \( a^{4} - 4 a^{2} + a + 2\) , \( 3 a^{5} - 15 a^{3} + 3 a^{2} + 15 a - 3\) , \( -a^{5} - 4 a^{4} + 2 a^{3} + 17 a^{2} - 18\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+5a\right){x}{y}+\left(a^{4}-4a^{2}+a+2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a+3\right){x}^{2}+\left(3a^{5}-15a^{3}+3a^{2}+15a-3\right){x}-a^{5}-4a^{4}+2a^{3}+17a^{2}-18$ |
| 27.1-a2 |
27.1-a |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17366.84056$ |
1.71926 |
\( -31774610286 a^{5} + 62583769395 a^{4} + 67381704855 a^{3} - 132716069946 a^{2} - 24571889838 a + 48397184451 \) |
\( \bigl[a^{5} - 4 a^{3} + a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 6 a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 3\) , \( -a^{5} + 4 a^{4} + 7 a^{3} - 19 a^{2} - 9 a + 21\) , \( -4 a^{5} + a^{4} + 23 a^{3} - 4 a^{2} - 27 a + 4\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-6a+3\right){x}^{2}+\left(-a^{5}+4a^{4}+7a^{3}-19a^{2}-9a+21\right){x}-4a^{5}+a^{4}+23a^{3}-4a^{2}-27a+4$ |
| 27.1-b1 |
27.1-b |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.057082274$ |
$90733.29985$ |
3.07639 |
\( -818991 a^{5} + 1040202 a^{4} + 3564270 a^{3} - 4511700 a^{2} - 1504170 a + 1853631 \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a - 1\) , \( a^{5} - 5 a^{3} + a^{2} + 5 a - 2\) , \( a^{5} - 3 a^{3} + 5 a^{2} + 3 a - 7\) , \( 3 a^{5} + 4 a^{4} - 12 a^{3} - 13 a^{2} + 12 a + 11\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{5}-5a^{3}+a^{2}+5a-2\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-6a-1\right){x}^{2}+\left(a^{5}-3a^{3}+5a^{2}+3a-7\right){x}+3a^{5}+4a^{4}-12a^{3}-13a^{2}+12a+11$ |
| 27.1-b2 |
27.1-b |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.171246822$ |
$1120.164195$ |
3.07639 |
\( -31774610286 a^{5} + 62583769395 a^{4} + 67381704855 a^{3} - 132716069946 a^{2} - 24571889838 a + 48397184451 \) |
\( \bigl[a^{2} - 1\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 2\) , \( a^{5} + a^{4} - 4 a^{3} - 5 a^{2} + 2 a + 5\) , \( 4 a^{4} - a^{3} - 20 a^{2} + a + 22\) , \( 3 a^{5} + 2 a^{4} - 17 a^{3} - 11 a^{2} + 19 a + 11\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-5a^{2}+2a+5\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a+2\right){x}^{2}+\left(4a^{4}-a^{3}-20a^{2}+a+22\right){x}+3a^{5}+2a^{4}-17a^{3}-11a^{2}+19a+11$ |
| 27.1-c1 |
27.1-c |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17366.84056$ |
1.71926 |
\( 140172878133 a^{5} - 180202777029 a^{4} - 609373044090 a^{3} + 783394877511 a^{2} + 254442862521 a - 327105431919 \) |
\( \bigl[a^{5} - 4 a^{3} + 2 a\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 3\) , \( a^{4} - 5 a^{2} + a + 4\) , \( 3 a^{5} + a^{4} - 16 a^{3} - a^{2} + 14 a + 3\) , \( -a^{5} + a^{4} + a^{3} - 3 a^{2} + a + 3\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+2a\right){x}{y}+\left(a^{4}-5a^{2}+a+4\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a+3\right){x}^{2}+\left(3a^{5}+a^{4}-16a^{3}-a^{2}+14a+3\right){x}-a^{5}+a^{4}+a^{3}-3a^{2}+a+3$ |
| 27.1-c2 |
27.1-c |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1929.648952$ |
1.71926 |
\( -998730 a^{5} - 689310 a^{4} + 5524335 a^{3} + 3797442 a^{2} - 6405966 a - 4387581 \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 6 a - 3\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 4 a + 2\) , \( -6 a^{5} - 7 a^{4} + 27 a^{3} + 32 a^{2} - 12 a - 12\) , \( 6 a^{5} + 8 a^{4} - 25 a^{3} - 34 a^{2} + 9 a + 14\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+4a+2\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+5a^{2}-6a-3\right){x}^{2}+\left(-6a^{5}-7a^{4}+27a^{3}+32a^{2}-12a-12\right){x}+6a^{5}+8a^{4}-25a^{3}-34a^{2}+9a+14$ |
| 27.1-d1 |
27.1-d |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.171246822$ |
$1120.164195$ |
3.07639 |
\( 140172878133 a^{5} - 180202777029 a^{4} - 609373044090 a^{3} + 783394877511 a^{2} + 254442862521 a - 327105431919 \) |
\( \bigl[a^{4} - 4 a^{2} + 3\) , \( -a^{5} + 6 a^{3} - 6 a\) , \( a^{2} + a - 1\) , \( 2 a^{4} - 5 a^{2} + 3\) , \( 2 a^{5} + a^{4} - 7 a^{3} - 2 a^{2} + 5 a - 1\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+3\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-6a\right){x}^{2}+\left(2a^{4}-5a^{2}+3\right){x}+2a^{5}+a^{4}-7a^{3}-2a^{2}+5a-1$ |
| 27.1-d2 |
27.1-d |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.057082274$ |
$90733.29985$ |
3.07639 |
\( -998730 a^{5} - 689310 a^{4} + 5524335 a^{3} + 3797442 a^{2} - 6405966 a - 4387581 \) |
\( \bigl[a^{2} - 2\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 6 a + 5\) , \( a^{5} - 5 a^{3} + 5 a\) , \( -4 a^{5} - 5 a^{4} + 14 a^{3} + 22 a^{2} + 3 a - 3\) , \( -11 a^{5} - 14 a^{4} + 46 a^{3} + 61 a^{2} - 15 a - 23\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{5}-5a^{3}+5a\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+6a+5\right){x}^{2}+\left(-4a^{5}-5a^{4}+14a^{3}+22a^{2}+3a-3\right){x}-11a^{5}-14a^{4}+46a^{3}+61a^{2}-15a-23$ |
| 27.1-e1 |
27.1-e |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1929.648952$ |
1.71926 |
\( 179739 a^{5} - 350892 a^{4} - 368010 a^{3} + 714258 a^{2} + 125631 a - 251721 \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 6 a - 3\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 3\) , \( a^{5} + 3 a^{4} - 5 a^{3} - 12 a^{2} + 7 a + 9\) , \( -2 a^{5} + 3 a^{4} + 13 a^{3} - 10 a^{2} - 19 a - 5\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+3\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+5a^{2}-6a-3\right){x}^{2}+\left(a^{5}+3a^{4}-5a^{3}-12a^{2}+7a+9\right){x}-2a^{5}+3a^{4}+13a^{3}-10a^{2}-19a-5$ |
| 27.1-e2 |
27.1-e |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17366.84056$ |
1.71926 |
\( -171947488419 a^{5} + 117619007634 a^{4} + 951228788670 a^{3} - 650678807565 a^{2} - 1102436871534 a + 754111230255 \) |
\( \bigl[a^{5} - 4 a^{3} + a\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 5 a^{2} + 4 a + 4\) , \( -17 a^{5} - 13 a^{4} + 94 a^{3} + 76 a^{2} - 113 a - 90\) , \( 108 a^{5} + 77 a^{4} - 598 a^{3} - 423 a^{2} + 691 a + 489\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-5a^{2}+4a+4\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+6a+3\right){x}^{2}+\left(-17a^{5}-13a^{4}+94a^{3}+76a^{2}-113a-90\right){x}+108a^{5}+77a^{4}-598a^{3}-423a^{2}+691a+489$ |
| 27.1-f1 |
27.1-f |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.057082274$ |
$90733.29985$ |
3.07639 |
\( 179739 a^{5} - 350892 a^{4} - 368010 a^{3} + 714258 a^{2} + 125631 a - 251721 \) |
\( \bigl[a^{2} - 2\) , \( a^{5} + a^{4} - 6 a^{3} - 5 a^{2} + 6 a + 5\) , \( a^{5} + a^{4} - 4 a^{3} - 5 a^{2} + 2 a + 4\) , \( 3 a^{5} + 6 a^{4} - 18 a^{3} - 27 a^{2} + 21 a + 22\) , \( 4 a^{5} + a^{4} - 24 a^{3} - 8 a^{2} + 31 a + 17\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-5a^{2}+2a+4\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-5a^{2}+6a+5\right){x}^{2}+\left(3a^{5}+6a^{4}-18a^{3}-27a^{2}+21a+22\right){x}+4a^{5}+a^{4}-24a^{3}-8a^{2}+31a+17$ |
| 27.1-f2 |
27.1-f |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.171246822$ |
$1120.164195$ |
3.07639 |
\( -171947488419 a^{5} + 117619007634 a^{4} + 951228788670 a^{3} - 650678807565 a^{2} - 1102436871534 a + 754111230255 \) |
\( \bigl[a^{2} - 1\) , \( -a^{5} + 6 a^{3} - a^{2} - 6 a + 2\) , \( a + 1\) , \( -20 a^{5} - 14 a^{4} + 110 a^{3} + 79 a^{2} - 127 a - 91\) , \( -127 a^{5} - 91 a^{4} + 703 a^{3} + 503 a^{2} - 815 a - 583\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-a^{2}-6a+2\right){x}^{2}+\left(-20a^{5}-14a^{4}+110a^{3}+79a^{2}-127a-91\right){x}-127a^{5}-91a^{4}+703a^{3}+503a^{2}-815a-583$ |
| 27.1-g1 |
27.1-g |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17366.84056$ |
1.71926 |
\( -140172878133 a^{5} - 180202777029 a^{4} + 609373044090 a^{3} + 783394877511 a^{2} - 254442862521 a - 327105431919 \) |
\( \bigl[a^{5} - 4 a^{3} + a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 6 a + 3\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -8 a^{5} + 43 a^{3} + 6 a^{2} - 43 a - 15\) , \( 15 a^{5} + 7 a^{4} - 80 a^{3} - 40 a^{2} + 87 a + 54\bigr] \) |
${y}^2+\left(a^{5}-4a^{3}+a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-6a+3\right){x}^{2}+\left(-8a^{5}+43a^{3}+6a^{2}-43a-15\right){x}+15a^{5}+7a^{4}-80a^{3}-40a^{2}+87a+54$ |
| 27.1-g2 |
27.1-g |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1929.648952$ |
1.71926 |
\( 998730 a^{5} - 689310 a^{4} - 5524335 a^{3} + 3797442 a^{2} + 6405966 a - 4387581 \) |
\( \bigl[a\) , \( a^{5} + a^{4} - 6 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{5} - 5 a^{3} + 4 a + 1\) , \( a^{5} - a^{4} - 7 a^{3} + 5 a^{2} + 6 a\) , \( -a^{5} + a^{4} + 4 a^{3} - 6 a^{2} - a + 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{5}-5a^{3}+4a+1\right){y}={x}^{3}+\left(a^{5}+a^{4}-6a^{3}-4a^{2}+6a+3\right){x}^{2}+\left(a^{5}-a^{4}-7a^{3}+5a^{2}+6a\right){x}-a^{5}+a^{4}+4a^{3}-6a^{2}-a+3$ |
| 27.1-h1 |
27.1-h |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.171246822$ |
$1120.164195$ |
3.07639 |
\( -140172878133 a^{5} - 180202777029 a^{4} + 609373044090 a^{3} + 783394877511 a^{2} - 254442862521 a - 327105431919 \) |
\( \bigl[a^{2} - 1\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 2\) , \( a^{5} - 4 a^{3} + a^{2} + a - 2\) , \( -6 a^{5} - a^{4} + 31 a^{3} + 9 a^{2} - 31 a - 16\) , \( -22 a^{5} - 7 a^{4} + 117 a^{3} + 45 a^{2} - 125 a - 70\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a+2\right){x}^{2}+\left(-6a^{5}-a^{4}+31a^{3}+9a^{2}-31a-16\right){x}-22a^{5}-7a^{4}+117a^{3}+45a^{2}-125a-70$ |
| 27.1-h2 |
27.1-h |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.057082274$ |
$90733.29985$ |
3.07639 |
\( 998730 a^{5} - 689310 a^{4} - 5524335 a^{3} + 3797442 a^{2} + 6405966 a - 4387581 \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( -a^{5} - a^{4} + 6 a^{3} + 4 a^{2} - 6 a - 1\) , \( a^{4} + a^{3} - 4 a^{2} - 3 a + 2\) , \( -2 a^{4} + 8 a^{2} - a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 10 a^{2} + a - 4\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}+\left(a^{4}+a^{3}-4a^{2}-3a+2\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+4a^{2}-6a-1\right){x}^{2}+\left(-2a^{4}+8a^{2}-a-1\right){x}+a^{5}-2a^{4}-5a^{3}+10a^{2}+a-4$ |
| 27.1-i1 |
27.1-i |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1929.648952$ |
1.71926 |
\( -179739 a^{5} - 350892 a^{4} + 368010 a^{3} + 714258 a^{2} - 125631 a - 251721 \) |
\( \bigl[a^{5} - 5 a^{3} + 5 a\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 3\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 3\) , \( -5 a^{5} + 6 a^{4} + 28 a^{3} - 31 a^{2} - 34 a + 36\) , \( 17 a^{5} - 11 a^{4} - 95 a^{3} + 60 a^{2} + 110 a - 69\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+5a\right){x}{y}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+3\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a+3\right){x}^{2}+\left(-5a^{5}+6a^{4}+28a^{3}-31a^{2}-34a+36\right){x}+17a^{5}-11a^{4}-95a^{3}+60a^{2}+110a-69$ |
| 27.1-i2 |
27.1-i |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17366.84056$ |
1.71926 |
\( 171947488419 a^{5} + 117619007634 a^{4} - 951228788670 a^{3} - 650678807565 a^{2} + 1102436871534 a + 754111230255 \) |
\( \bigl[a^{5} - 5 a^{3} + 4 a\) , \( -a^{5} + 6 a^{3} - a^{2} - 6 a + 3\) , \( a^{4} - 4 a^{2} + 3\) , \( 3 a^{5} - 10 a^{4} + a^{3} + 21 a^{2} - 9 a - 3\) , \( -39 a^{5} + 72 a^{4} + 87 a^{3} - 153 a^{2} - 36 a + 58\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+4a\right){x}{y}+\left(a^{4}-4a^{2}+3\right){y}={x}^{3}+\left(-a^{5}+6a^{3}-a^{2}-6a+3\right){x}^{2}+\left(3a^{5}-10a^{4}+a^{3}+21a^{2}-9a-3\right){x}-39a^{5}+72a^{4}+87a^{3}-153a^{2}-36a+58$ |
| 27.1-j1 |
27.1-j |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.057082274$ |
$90733.29985$ |
3.07639 |
\( -179739 a^{5} - 350892 a^{4} + 368010 a^{3} + 714258 a^{2} - 125631 a - 251721 \) |
\( \bigl[a^{4} - 4 a^{2} + 2\) , \( -a^{5} + 6 a^{3} + a^{2} - 6 a - 1\) , \( a^{5} - 4 a^{3} + 2 a\) , \( -6 a^{5} + 6 a^{4} + 35 a^{3} - 29 a^{2} - 42 a + 33\) , \( -23 a^{5} + 17 a^{4} + 129 a^{3} - 91 a^{2} - 150 a + 103\bigr] \) |
${y}^2+\left(a^{4}-4a^{2}+2\right){x}{y}+\left(a^{5}-4a^{3}+2a\right){y}={x}^{3}+\left(-a^{5}+6a^{3}+a^{2}-6a-1\right){x}^{2}+\left(-6a^{5}+6a^{4}+35a^{3}-29a^{2}-42a+33\right){x}-23a^{5}+17a^{4}+129a^{3}-91a^{2}-150a+103$ |
| 27.1-j2 |
27.1-j |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.171246822$ |
$1120.164195$ |
3.07639 |
\( 171947488419 a^{5} + 117619007634 a^{4} - 951228788670 a^{3} - 650678807565 a^{2} + 1102436871534 a + 754111230255 \) |
\( \bigl[a^{2} - 2\) , \( a^{5} - 6 a^{3} + a^{2} + 6 a - 1\) , \( a^{5} - 4 a^{3} + a^{2} + 2 a - 2\) , \( 5 a^{5} - 10 a^{4} - 12 a^{3} + 23 a^{2} + 5 a - 8\) , \( 43 a^{5} - 82 a^{4} - 93 a^{3} + 174 a^{2} + 35 a - 64\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+2a-2\right){y}={x}^{3}+\left(a^{5}-6a^{3}+a^{2}+6a-1\right){x}^{2}+\left(5a^{5}-10a^{4}-12a^{3}+23a^{2}+5a-8\right){x}+43a^{5}-82a^{4}-93a^{3}+174a^{2}+35a-64$ |
| 27.1-k1 |
27.1-k |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$1929.648952$ |
1.71926 |
\( 818991 a^{5} + 1040202 a^{4} - 3564270 a^{3} - 4511700 a^{2} + 1504170 a + 1853631 \) |
\( \bigl[a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 6 a + 3\) , \( a\) , \( -a^{5} + 4 a^{4} + 4 a^{3} - 10 a^{2} - 5 a + 6\) , \( 4 a^{5} - 6 a^{4} - 7 a^{3} + 11 a^{2} + a - 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-4a^{2}-6a+3\right){x}^{2}+\left(-a^{5}+4a^{4}+4a^{3}-10a^{2}-5a+6\right){x}+4a^{5}-6a^{4}-7a^{3}+11a^{2}+a-3$ |
| 27.1-k2 |
27.1-k |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$17366.84056$ |
1.71926 |
\( 31774610286 a^{5} + 62583769395 a^{4} - 67381704855 a^{3} - 132716069946 a^{2} + 24571889838 a + 48397184451 \) |
\( \bigl[a^{3} - 2 a\) , \( a^{5} - 6 a^{3} - a^{2} + 6 a + 3\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 27 a^{2} + 2 a + 15\) , \( 6 a^{5} - 6 a^{4} - 28 a^{3} + 26 a^{2} + 15 a - 9\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{5}-6a^{3}-a^{2}+6a+3\right){x}^{2}+\left(-3a^{5}+6a^{4}+10a^{3}-27a^{2}+2a+15\right){x}+6a^{5}-6a^{4}-28a^{3}+26a^{2}+15a-9$ |
| 27.1-l1 |
27.1-l |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.057082274$ |
$90733.29985$ |
3.07639 |
\( 818991 a^{5} + 1040202 a^{4} - 3564270 a^{3} - 4511700 a^{2} + 1504170 a + 1853631 \) |
\( \bigl[a^{4} - 5 a^{2} + 4\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 6 a - 1\) , \( 0\) , \( a^{5} + 2 a^{4} - 8 a^{3} - 2 a^{2} + 7 a + 3\) , \( -4 a^{5} + 9 a^{4} + 5 a^{3} - 17 a^{2} + 7\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+4\right){x}{y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+6a-1\right){x}^{2}+\left(a^{5}+2a^{4}-8a^{3}-2a^{2}+7a+3\right){x}-4a^{5}+9a^{4}+5a^{3}-17a^{2}+7$ |
| 27.1-l2 |
27.1-l |
$2$ |
$3$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$131.99409$ |
$(a^5-5a^3+4a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.171246822$ |
$1120.164195$ |
3.07639 |
\( 31774610286 a^{5} + 62583769395 a^{4} - 67381704855 a^{3} - 132716069946 a^{2} + 24571889838 a + 48397184451 \) |
\( \bigl[a^{4} - 5 a^{2} + 5\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 6 a - 4\) , \( a^{5} + a^{4} - 4 a^{3} - 5 a^{2} + a + 4\) , \( -4 a^{5} + 5 a^{4} + 18 a^{3} - 21 a^{2} - 7 a + 8\) , \( -9 a^{5} + 13 a^{4} + 40 a^{3} - 57 a^{2} - 17 a + 23\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+5\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(-a^{5}-a^{4}+6a^{3}+5a^{2}-6a-4\right){x}^{2}+\left(-4a^{5}+5a^{4}+18a^{3}-21a^{2}-7a+8\right){x}-9a^{5}+13a^{4}+40a^{3}-57a^{2}-17a+23$ |
| 37.1-a1 |
37.1-a |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{3} \) |
$135.50573$ |
$(-a^5-a^4+4a^3+5a^2-a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$0.686236352$ |
$1196.823785$ |
3.29292 |
\( -\frac{20373857822344320}{50653} a^{5} - \frac{26192115989398656}{50653} a^{4} + \frac{88571233431522432}{50653} a^{3} + \frac{113864960362929984}{50653} a^{2} - \frac{36982795629076992}{50653} a - \frac{47544157222489152}{50653} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{3} - 2 a + 1\) , \( -10 a^{5} + 11 a^{4} + 42 a^{3} - 47 a^{2} - 15 a + 21\) , \( -21 a^{5} + 25 a^{4} + 91 a^{3} - 110 a^{2} - 39 a + 47\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-1\right){x}^{2}+\left(-10a^{5}+11a^{4}+42a^{3}-47a^{2}-15a+21\right){x}-21a^{5}+25a^{4}+91a^{3}-110a^{2}-39a+47$ |
| 37.1-a2 |
37.1-a |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{6} \) |
$135.50573$ |
$(-a^5-a^4+4a^3+5a^2-a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.343118176$ |
$1196.823785$ |
3.29292 |
\( \frac{512387785726848}{2565726409} a^{5} + \frac{1013205729373632}{2565726409} a^{4} - \frac{2439816928136064}{2565726409} a^{3} - \frac{3969618093218880}{2565726409} a^{2} + \frac{985089238692480}{2565726409} a + \frac{1675217974587264}{2565726409} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( -a^{4} + 4 a^{2} + a - 1\) , \( a^{5} - 4 a^{3} + 2 a + 1\) , \( 4 a^{5} + 4 a^{4} - 18 a^{3} - 23 a^{2} + 7 a + 11\) , \( 23 a^{5} + 27 a^{4} - 102 a^{3} - 127 a^{2} + 43 a + 53\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{5}-4a^{3}+2a+1\right){y}={x}^{3}+\left(-a^{4}+4a^{2}+a-1\right){x}^{2}+\left(4a^{5}+4a^{4}-18a^{3}-23a^{2}+7a+11\right){x}+23a^{5}+27a^{4}-102a^{3}-127a^{2}+43a+53$ |
| 37.1-a3 |
37.1-a |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$135.50573$ |
$(-a^5-a^4+4a^3+5a^2-a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.114372725$ |
$96942.72665$ |
3.29292 |
\( \frac{835007616}{1369} a^{5} + \frac{759865536}{1369} a^{4} - \frac{4222938240}{1369} a^{3} - \frac{3419371584}{1369} a^{2} + \frac{4698601344}{1369} a + \frac{3575650176}{1369} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 4\) , \( -a^{5} - a^{4} + 4 a^{3} + 6 a^{2} - 2 a - 7\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + a + 3\) , \( -a^{4} - 2 a^{3} + 5 a^{2} + 3 a - 2\) , \( -a^{5} + 3 a^{4} + 6 a^{3} - 13 a^{2} - 9 a + 9\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+4\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{5}-a^{4}+4a^{3}+6a^{2}-2a-7\right){x}^{2}+\left(-a^{4}-2a^{3}+5a^{2}+3a-2\right){x}-a^{5}+3a^{4}+6a^{3}-13a^{2}-9a+9$ |
| 37.1-a4 |
37.1-a |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$135.50573$ |
$(-a^5-a^4+4a^3+5a^2-a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$0.228745450$ |
$96942.72665$ |
3.29292 |
\( -\frac{84211166592}{37} a^{5} + \frac{57602524032}{37} a^{4} + \frac{465865831296}{37} a^{3} - \frac{318665285568}{37} a^{2} - \frac{539926124544}{37} a + \frac{369328794048}{37} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( -a^{4} + 6 a^{2} + a - 7\) , \( a^{5} - 5 a^{3} + a^{2} + 4 a - 1\) , \( -14 a^{5} - 9 a^{4} + 78 a^{3} + 50 a^{2} - 91 a - 57\) , \( 85 a^{5} + 58 a^{4} - 470 a^{3} - 321 a^{2} + 545 a + 371\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}{y}+\left(a^{5}-5a^{3}+a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{4}+6a^{2}+a-7\right){x}^{2}+\left(-14a^{5}-9a^{4}+78a^{3}+50a^{2}-91a-57\right){x}+85a^{5}+58a^{4}-470a^{3}-321a^{2}+545a+371$ |
| 37.1-b1 |
37.1-b |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{3} \) |
$135.50573$ |
$(-a^5-a^4+4a^3+5a^2-a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.159070128$ |
$46928.16332$ |
3.32550 |
\( -\frac{20373857822344320}{50653} a^{5} - \frac{26192115989398656}{50653} a^{4} + \frac{88571233431522432}{50653} a^{3} + \frac{113864960362929984}{50653} a^{2} - \frac{36982795629076992}{50653} a - \frac{47544157222489152}{50653} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{3} - a^{2} + a + 2\) , \( a^{5} + a^{4} - 4 a^{3} - 4 a^{2} + a + 3\) , \( -8 a^{5} + 12 a^{4} + 35 a^{3} - 54 a^{2} - 16 a + 26\) , \( 13 a^{5} - 14 a^{4} - 58 a^{3} + 61 a^{2} + 29 a - 27\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-4a^{2}+a+3\right){y}={x}^{3}+\left(a^{5}-4a^{3}-a^{2}+a+2\right){x}^{2}+\left(-8a^{5}+12a^{4}+35a^{3}-54a^{2}-16a+26\right){x}+13a^{5}-14a^{4}-58a^{3}+61a^{2}+29a-27$ |
| 37.1-b2 |
37.1-b |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{6} \) |
$135.50573$ |
$(-a^5-a^4+4a^3+5a^2-a-4)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.079535064$ |
$46928.16332$ |
3.32550 |
\( \frac{512387785726848}{2565726409} a^{5} + \frac{1013205729373632}{2565726409} a^{4} - \frac{2439816928136064}{2565726409} a^{3} - \frac{3969618093218880}{2565726409} a^{2} + \frac{985089238692480}{2565726409} a + \frac{1675217974587264}{2565726409} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 4 a + 2\) , \( a^{5} + a^{4} - 4 a^{3} - 5 a^{2} + a + 5\) , \( 5 a^{5} + 7 a^{4} - 22 a^{3} - 36 a^{2} + 7 a + 18\) , \( -18 a^{5} - 22 a^{4} + 79 a^{3} + 100 a^{2} - 32 a - 44\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+4a+2\right){x}^{2}+\left(5a^{5}+7a^{4}-22a^{3}-36a^{2}+7a+18\right){x}-18a^{5}-22a^{4}+79a^{3}+100a^{2}-32a-44$ |
| 37.1-b3 |
37.1-b |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37^{2} \) |
$135.50573$ |
$(-a^5-a^4+4a^3+5a^2-a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.238605192$ |
$5214.240369$ |
3.32550 |
\( \frac{835007616}{1369} a^{5} + \frac{759865536}{1369} a^{4} - \frac{4222938240}{1369} a^{3} - \frac{3419371584}{1369} a^{2} + \frac{4698601344}{1369} a + \frac{3575650176}{1369} \) |
\( \bigl[a^{4} - 5 a^{2} + a + 4\) , \( a^{4} + a^{3} - 6 a^{2} - 2 a + 5\) , \( a^{5} - 4 a^{3} + a^{2} + 2 a - 1\) , \( -a^{4} - 2 a^{3} + 4 a^{2} + 3 a\) , \( a^{5} - 2 a^{4} - 7 a^{3} + 7 a^{2} + 10 a - 7\bigr] \) |
${y}^2+\left(a^{4}-5a^{2}+a+4\right){x}{y}+\left(a^{5}-4a^{3}+a^{2}+2a-1\right){y}={x}^{3}+\left(a^{4}+a^{3}-6a^{2}-2a+5\right){x}^{2}+\left(-a^{4}-2a^{3}+4a^{2}+3a\right){x}+a^{5}-2a^{4}-7a^{3}+7a^{2}+10a-7$ |
| 37.1-b4 |
37.1-b |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.1 |
\( 37 \) |
\( 37 \) |
$135.50573$ |
$(-a^5-a^4+4a^3+5a^2-a-4)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$0.477210384$ |
$5214.240369$ |
3.32550 |
\( -\frac{84211166592}{37} a^{5} + \frac{57602524032}{37} a^{4} + \frac{465865831296}{37} a^{3} - \frac{318665285568}{37} a^{2} - \frac{539926124544}{37} a + \frac{369328794048}{37} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{4} - 6 a^{2} + a + 5\) , \( a^{4} - 5 a^{2} + a + 5\) , \( -14 a^{5} - 9 a^{4} + 76 a^{3} + 50 a^{2} - 88 a - 57\) , \( -94 a^{5} - 65 a^{4} + 520 a^{3} + 358 a^{2} - 602 a - 415\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}{y}+\left(a^{4}-5a^{2}+a+5\right){y}={x}^{3}+\left(a^{4}-6a^{2}+a+5\right){x}^{2}+\left(-14a^{5}-9a^{4}+76a^{3}+50a^{2}-88a-57\right){x}-94a^{5}-65a^{4}+520a^{3}+358a^{2}-602a-415$ |
| 37.2-a1 |
37.2-a |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.2 |
\( 37 \) |
\( 37^{6} \) |
$135.50573$ |
$(a^5-5a^3-a^2+4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.343118176$ |
$1196.823785$ |
3.29292 |
\( -\frac{1210483688447232}{2565726409} a^{5} - \frac{1096410553649280}{2565726409} a^{4} + \frac{6174540442734336}{2565726409} a^{3} + \frac{5398847943970752}{2565726409} a^{2} - \frac{5720688541010304}{2565726409} a - \frac{4404016401654528}{2565726409} \) |
\( \bigl[a^{4} + a^{3} - 5 a^{2} - 2 a + 5\) , \( a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} + a^{4} - 4 a^{3} - 5 a^{2} + a + 4\) , \( -a^{5} - 2 a^{4} + a^{3} + 3 a^{2} + a - 3\) , \( -10 a^{5} - 19 a^{4} + 22 a^{3} + 39 a^{2} - 11 a - 17\bigr] \) |
${y}^2+\left(a^{4}+a^{3}-5a^{2}-2a+5\right){x}{y}+\left(a^{5}+a^{4}-4a^{3}-5a^{2}+a+4\right){y}={x}^{3}+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}^{2}+\left(-a^{5}-2a^{4}+a^{3}+3a^{2}+a-3\right){x}-10a^{5}-19a^{4}+22a^{3}+39a^{2}-11a-17$ |
| 37.2-a2 |
37.2-a |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.2 |
\( 37 \) |
\( 37^{2} \) |
$135.50573$ |
$(a^5-5a^3-a^2+4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.114372725$ |
$96942.72665$ |
3.29292 |
\( \frac{379862784}{1369} a^{5} - \frac{379956096}{1369} a^{4} - \frac{1947214080}{1369} a^{3} + \frac{2279689920}{1369} a^{2} + \frac{828144000}{1369} a - \frac{983543040}{1369} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( -a^{4} - a^{3} + 6 a^{2} + 4 a - 7\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -3 a^{5} + a^{4} + 14 a^{3} - 7 a^{2} - 11 a + 9\) , \( -3 a^{4} + 14 a^{2} - a - 11\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(-a^{4}-a^{3}+6a^{2}+4a-7\right){x}^{2}+\left(-3a^{5}+a^{4}+14a^{3}-7a^{2}-11a+9\right){x}-3a^{4}+14a^{2}-a-11$ |
| 37.2-a3 |
37.2-a |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.2 |
\( 37 \) |
\( 37 \) |
$135.50573$ |
$(a^5-5a^3-a^2+4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$0.228745450$ |
$96942.72665$ |
3.29292 |
\( \frac{15559703424}{37} a^{5} + \frac{30652665408}{37} a^{4} - \frac{32988518784}{37} a^{3} - \frac{65008137600}{37} a^{2} + \frac{12019985280}{37} a + \frac{23713649856}{37} \) |
\( \bigl[a^{5} - 5 a^{3} + a^{2} + 4 a - 2\) , \( -a^{5} - a^{4} + 5 a^{3} + 6 a^{2} - 5 a - 7\) , \( a^{4} - 5 a^{2} + 5\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 13 a^{2} - 2 a + 7\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 9 a^{2} - 4\bigr] \) |
${y}^2+\left(a^{5}-5a^{3}+a^{2}+4a-2\right){x}{y}+\left(a^{4}-5a^{2}+5\right){y}={x}^{3}+\left(-a^{5}-a^{4}+5a^{3}+6a^{2}-5a-7\right){x}^{2}+\left(-2a^{5}+3a^{4}+8a^{3}-13a^{2}-2a+7\right){x}+a^{5}-2a^{4}-4a^{3}+9a^{2}-4$ |
| 37.2-a4 |
37.2-a |
$4$ |
$6$ |
\(\Q(\zeta_{36})^+\) |
$6$ |
$[6, 0]$ |
37.2 |
\( 37 \) |
\( 37^{3} \) |
$135.50573$ |
$(a^5-5a^3-a^2+4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$0.686236352$ |
$1196.823785$ |
3.29292 |
\( \frac{24992326442047104}{50653} a^{5} + \frac{17095619584063296}{50653} a^{4} - \frac{138259687890434688}{50653} a^{3} - \frac{94574594325651840}{50653} a^{2} + \frac{160237330631130240}{50653} a + \frac{109608538713902784}{50653} \) |
\( \bigl[a^{5} + a^{4} - 5 a^{3} - 4 a^{2} + 5 a + 2\) , \( a^{5} - a^{4} - 6 a^{3} + 4 a^{2} + 7 a - 1\) , \( a^{5} - 4 a^{3} + a + 1\) , \( 12 a^{5} - 8 a^{4} - 67 a^{3} + 42 a^{2} + 77 a - 44\) , \( 24 a^{5} - 15 a^{4} - 134 a^{3} + 85 a^{2} + 159 a - 103\bigr] \) |
${y}^2+\left(a^{5}+a^{4}-5a^{3}-4a^{2}+5a+2\right){x}{y}+\left(a^{5}-4a^{3}+a+1\right){y}={x}^{3}+\left(a^{5}-a^{4}-6a^{3}+4a^{2}+7a-1\right){x}^{2}+\left(12a^{5}-8a^{4}-67a^{3}+42a^{2}+77a-44\right){x}+24a^{5}-15a^{4}-134a^{3}+85a^{2}+159a-103$ |
*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.
