| 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 |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$21.26627$ |
$(a^2-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$386.5609799$ |
1.01171790 |
\( \frac{1246362404}{81} a^{4} - \frac{1041117076}{27} a^{3} - \frac{719458786}{27} a^{2} + \frac{7323102649}{81} a - \frac{2459871980}{81} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 106 a^{4} - 70 a^{3} - 413 a^{2} - 23 a + 81\) , \( 2837 a^{4} - 1889 a^{3} - 11031 a^{2} - 533 a + 2126\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a+2\right){x}^{2}+\left(106a^{4}-70a^{3}-413a^{2}-23a+81\right){x}+2837a^{4}-1889a^{3}-11031a^{2}-533a+2126$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{30} \) |
$21.26627$ |
$(a^2-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$193.2804899$ |
1.01171790 |
\( \frac{42958432423020244475506}{282429536481} a^{4} + \frac{4551898895594886045259}{94143178827} a^{3} - \frac{32400118789856343855629}{94143178827} a^{2} - \frac{10536177229996279192588}{282429536481} a + \frac{18530426122247352513662}{282429536481} \) |
\( \bigl[a\) , \( -a^{3} + 5 a\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 76 a^{4} - 83 a^{3} - 258 a^{2} + 73 a - 19\) , \( -302 a^{4} + 116 a^{3} + 1335 a^{2} + 348 a - 480\bigr] \) |
${y}^2+a{x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(76a^{4}-83a^{3}-258a^{2}+73a-19\right){x}-302a^{4}+116a^{3}+1335a^{2}+348a-480$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$21.26627$ |
$(a^2-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$386.5609799$ |
1.01171790 |
\( \frac{679068463130598740}{531441} a^{4} - \frac{359821343885971159}{177147} a^{3} - \frac{826730295123875959}{177147} a^{2} + \frac{2377533227165763589}{531441} a + \frac{1654749596218451752}{531441} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - a - 2\) , \( -a^{4} - 2 a^{3} + 6 a^{2} + 8 a - 11\) , \( 36 a^{4} - 88 a^{3} - 60 a^{2} + 206 a - 75\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(-a^{4}-2a^{3}+6a^{2}+8a-11\right){x}+36a^{4}-88a^{3}-60a^{2}+206a-75$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{14} \) |
$21.26627$ |
$(a^2-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$193.2804899$ |
1.01171790 |
\( -\frac{7766624836025326355}{6561} a^{4} + \frac{6488464292861171239}{2187} a^{3} + \frac{4481598027790652077}{2187} a^{2} - \frac{45640052133196144267}{6561} a + \frac{15340352105491554221}{6561} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 8 a + 3\) , \( a^{2} - a - 3\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 71 a^{4} - 36 a^{3} - 299 a^{2} - 24 a + 56\) , \( 497 a^{4} - 316 a^{3} - 1964 a^{2} - 104 a + 377\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-7a^{2}+8a+3\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(71a^{4}-36a^{3}-299a^{2}-24a+56\right){x}+497a^{4}-316a^{3}-1964a^{2}-104a+377$ |
| 9.1-b1 |
9.1-b |
$4$ |
$6$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$21.26627$ |
$(a^2-1)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$3087.086684$ |
0.897734128 |
\( \frac{1246362404}{81} a^{4} - \frac{1041117076}{27} a^{3} - \frac{719458786}{27} a^{2} + \frac{7323102649}{81} a - \frac{2459871980}{81} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + a - 1\) , \( 0\) , \( 2 a^{2} - a\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+a-1\right){x}^{2}+\left(2a^{2}-a\right){x}$ |
| 9.1-b2 |
9.1-b |
$4$ |
$6$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{30} \) |
$21.26627$ |
$(a^2-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$19.05609064$ |
0.897734128 |
\( \frac{42958432423020244475506}{282429536481} a^{4} + \frac{4551898895594886045259}{94143178827} a^{3} - \frac{32400118789856343855629}{94143178827} a^{2} - \frac{10536177229996279192588}{282429536481} a + \frac{18530426122247352513662}{282429536481} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( 9 a^{4} + 38 a^{3} - 125 a^{2} - 29 a + 5\) , \( -52 a^{4} + 394 a^{3} - 503 a^{2} - 335 a + 53\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){x}^{2}+\left(9a^{4}+38a^{3}-125a^{2}-29a+5\right){x}-52a^{4}+394a^{3}-503a^{2}-335a+53$ |
| 9.1-b3 |
9.1-b |
$4$ |
$6$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$21.26627$ |
$(a^2-1)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$38.11218129$ |
0.897734128 |
\( \frac{679068463130598740}{531441} a^{4} - \frac{359821343885971159}{177147} a^{3} - \frac{826730295123875959}{177147} a^{2} + \frac{2377533227165763589}{531441} a + \frac{1654749596218451752}{531441} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -11 a^{4} + 18 a^{3} + 35 a^{2} - 29 a - 20\) , \( -37 a^{4} + 72 a^{3} + 122 a^{2} - 163 a - 101\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){x}^{2}+\left(-11a^{4}+18a^{3}+35a^{2}-29a-20\right){x}-37a^{4}+72a^{3}+122a^{2}-163a-101$ |
| 9.1-b4 |
9.1-b |
$4$ |
$6$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{14} \) |
$21.26627$ |
$(a^2-1)$ |
$0$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$1543.543342$ |
0.897734128 |
\( -\frac{7766624836025326355}{6561} a^{4} + \frac{6488464292861171239}{2187} a^{3} + \frac{4481598027790652077}{2187} a^{2} - \frac{45640052133196144267}{6561} a + \frac{15340352105491554221}{6561} \) |
\( \bigl[a + 1\) , \( a^{4} - a^{3} - 3 a^{2} + a - 1\) , \( 0\) , \( -8 a^{2} + 4 a\) , \( -14 a^{4} + 5 a^{3} + 40 a^{2} - 7 a - 4\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{4}-a^{3}-3a^{2}+a-1\right){x}^{2}+\left(-8a^{2}+4a\right){x}-14a^{4}+5a^{3}+40a^{2}-7a-4$ |
| 13.1-a1 |
13.1-a |
$2$ |
$2$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{4} \) |
$22.06284$ |
$(a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$284.1162727$ |
1.48719366 |
\( -\frac{8844242842144}{28561} a^{4} + \frac{3901184928560}{28561} a^{3} + \frac{38808172739465}{28561} a^{2} + \frac{2512399121799}{28561} a - \frac{7585403021016}{28561} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 9 a + 4\) , \( a\) , \( 53 a^{4} - 87 a^{3} - 190 a^{2} + 191 a + 122\) , \( 579 a^{4} - 931 a^{3} - 2120 a^{2} + 2049 a + 1416\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+3\right){x}{y}+a{y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+9a+4\right){x}^{2}+\left(53a^{4}-87a^{3}-190a^{2}+191a+122\right){x}+579a^{4}-931a^{3}-2120a^{2}+2049a+1416$ |
| 13.1-a2 |
13.1-a |
$2$ |
$2$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
13.1 |
\( 13 \) |
\( 13^{2} \) |
$22.06284$ |
$(a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$568.2325455$ |
1.48719366 |
\( \frac{1596793}{169} a^{4} - \frac{937970}{169} a^{3} - \frac{7191975}{169} a^{2} + \frac{918304}{169} a + \frac{2080992}{169} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( -a^{2} + 2 a + 1\) , \( a^{2} - a - 2\) , \( 4 a^{4} - 6 a^{3} - 13 a^{2} + 10 a + 6\) , \( 5 a^{4} - 4 a^{3} - 19 a^{2} + 2 a + 3\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(4a^{4}-6a^{3}-13a^{2}+10a+6\right){x}+5a^{4}-4a^{3}-19a^{2}+2a+3$ |
| 13.1-b1 |
13.1-b |
$2$ |
$2$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{4} \) |
$22.06284$ |
$(a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.007774790$ |
$11246.94631$ |
1.14428645 |
\( -\frac{8844242842144}{28561} a^{4} + \frac{3901184928560}{28561} a^{3} + \frac{38808172739465}{28561} a^{2} + \frac{2512399121799}{28561} a - \frac{7585403021016}{28561} \) |
\( \bigl[1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 6 a + 2\) , \( 0\) , \( 8 a^{4} - 12 a^{3} - 28 a^{2} + 24 a + 12\) , \( 10 a^{4} - 19 a^{3} - 39 a^{2} + 50 a + 43\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(2a^{4}-3a^{3}-7a^{2}+6a+2\right){x}^{2}+\left(8a^{4}-12a^{3}-28a^{2}+24a+12\right){x}+10a^{4}-19a^{3}-39a^{2}+50a+43$ |
| 13.1-b2 |
13.1-b |
$2$ |
$2$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
13.1 |
\( 13 \) |
\( 13^{2} \) |
$22.06284$ |
$(a^3-3a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.003887395$ |
$22493.89263$ |
1.14428645 |
\( \frac{1596793}{169} a^{4} - \frac{937970}{169} a^{3} - \frac{7191975}{169} a^{2} + \frac{918304}{169} a + \frac{2080992}{169} \) |
\( \bigl[1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 6 a + 2\) , \( 0\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 6 a - 3\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(2a^{4}-3a^{3}-7a^{2}+6a+2\right){x}^{2}+\left(-2a^{4}+3a^{3}+7a^{2}-6a-3\right){x}$ |
| 25.1-a1 |
25.1-a |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$1769.528882$ |
1.15781477 |
\( \frac{708112}{25} a^{4} - \frac{1125079}{25} a^{3} - \frac{2581192}{25} a^{2} + \frac{496376}{5} a + \frac{1711623}{25} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 5\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( 2 a^{4} - 2 a^{3} - 4 a^{2} + 4 a\) , \( 2 a^{4} - a^{3} - 5 a^{2} + 2 a\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+8a^{2}-7a-5\right){x}^{2}+\left(2a^{4}-2a^{3}-4a^{2}+4a\right){x}+2a^{4}-a^{3}-5a^{2}+2a$ |
| 25.1-a2 |
25.1-a |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$884.7644411$ |
1.15781477 |
\( \frac{1549868991089}{625} a^{4} - \frac{2463604541892}{625} a^{3} - \frac{5660845609864}{625} a^{2} + \frac{5425940335044}{625} a + \frac{3777390596864}{625} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( 20 a^{4} - 18 a^{3} - 76 a^{2} + 10 a + 20\) , \( 69 a^{4} - 48 a^{3} - 268 a^{2} - 6 a + 54\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){y}={x}^{3}+\left(a^{4}-a^{3}-5a^{2}+4a+4\right){x}^{2}+\left(20a^{4}-18a^{3}-76a^{2}+10a+20\right){x}+69a^{4}-48a^{3}-268a^{2}-6a+54$ |
| 25.1-a3 |
25.1-a |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{16} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$27.64888878$ |
1.15781477 |
\( -\frac{136402392772743238}{390625} a^{4} + \frac{341339187700279242}{390625} a^{3} + \frac{236740655090238193}{390625} a^{2} - \frac{799831738588792786}{390625} a + \frac{268640638721913956}{390625} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -5 a^{4} - 14 a^{3} - 11 a^{2} + 55 a - 20\) , \( -63 a^{4} - 115 a^{3} + 166 a^{2} + 193 a - 100\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-4\right){x}^{2}+\left(-5a^{4}-14a^{3}-11a^{2}+55a-20\right){x}-63a^{4}-115a^{3}+166a^{2}+193a-100$ |
| 25.1-a4 |
25.1-a |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$442.3822205$ |
1.15781477 |
\( \frac{488509962822731359638}{25} a^{4} - \frac{776547463172625188346}{25} a^{3} - \frac{1784205847864588683433}{25} a^{2} + \frac{342071130235394451034}{5} a + \frac{1190397818850374480652}{25} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a - 2\) , \( a^{2} - 1\) , \( -53 a^{4} + 93 a^{3} + 155 a^{2} - 135 a - 149\) , \( -157 a^{4} + 112 a^{3} + 991 a^{2} - 666 a - 644\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-4a-2\right){x}^{2}+\left(-53a^{4}+93a^{3}+155a^{2}-135a-149\right){x}-157a^{4}+112a^{3}+991a^{2}-666a-644$ |
| 25.1-b1 |
25.1-b |
$1$ |
$1$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$424.5187979$ |
2.22212427 |
\( -\frac{1476597}{5} a^{4} + \frac{213601}{5} a^{3} + \frac{3235067}{5} a^{2} - \frac{577692}{5} a - \frac{972922}{5} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{4} - a^{3} - 3 a^{2} + a + 1\) , \( -28 a^{4} + 44 a^{3} + 105 a^{2} - 98 a - 72\) , \( 137 a^{4} - 218 a^{3} - 500 a^{2} + 480 a + 332\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+3a+2\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){x}^{2}+\left(-28a^{4}+44a^{3}+105a^{2}-98a-72\right){x}+137a^{4}-218a^{3}-500a^{2}+480a+332$ |
| 25.1-c1 |
25.1-c |
$1$ |
$1$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{2} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.001191585$ |
$36862.41352$ |
1.14960935 |
\( -\frac{1476597}{5} a^{4} + \frac{213601}{5} a^{3} + \frac{3235067}{5} a^{2} - \frac{577692}{5} a - \frac{972922}{5} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 1\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 1\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 6 a + 1\) , \( -2 a^{4} + 4 a^{3} + 8 a^{2} - 11 a - 8\) , \( 2 a^{4} - 6 a^{3} - 6 a^{2} + 17 a + 7\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+1\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+6a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-6a-1\right){x}^{2}+\left(-2a^{4}+4a^{3}+8a^{2}-11a-8\right){x}+2a^{4}-6a^{3}-6a^{2}+17a+7$ |
| 25.1-d1 |
25.1-d |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.200199043$ |
$2693.592912$ |
1.76419015 |
\( \frac{708112}{25} a^{4} - \frac{1125079}{25} a^{3} - \frac{2581192}{25} a^{2} + \frac{496376}{5} a + \frac{1711623}{25} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{2} - 1\) , \( 3 a^{4} - 6 a^{3} - 10 a^{2} + 13 a + 6\) , \( -20 a^{4} + 12 a^{3} + 77 a^{2} + 9 a - 11\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+3\right){x}^{2}+\left(3a^{4}-6a^{3}-10a^{2}+13a+6\right){x}-20a^{4}+12a^{3}+77a^{2}+9a-11$ |
| 25.1-d2 |
25.1-d |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{8} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.400398087$ |
$1346.796456$ |
1.76419015 |
\( \frac{1549868991089}{625} a^{4} - \frac{2463604541892}{625} a^{3} - \frac{5660845609864}{625} a^{2} + \frac{5425940335044}{625} a + \frac{3777390596864}{625} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( -a^{2} + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 5 a - 1\) , \( -8 a^{4} - 21 a^{3} + 15 a^{2} + 40 a - 7\) , \( -51 a^{4} - 10 a^{3} + 111 a^{2} - a - 9\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{2}+1\right){x}^{2}+\left(-8a^{4}-21a^{3}+15a^{2}+40a-7\right){x}-51a^{4}-10a^{3}+111a^{2}-a-9$ |
| 25.1-d3 |
25.1-d |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( - 5^{16} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.200199043$ |
$673.3982280$ |
1.76419015 |
\( -\frac{136402392772743238}{390625} a^{4} + \frac{341339187700279242}{390625} a^{3} + \frac{236740655090238193}{390625} a^{2} - \frac{799831738588792786}{390625} a + \frac{268640638721913956}{390625} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 1\) , \( a^{2} - 2\) , \( 89 a^{4} - 17 a^{3} - 439 a^{2} - 38 a + 86\) , \( -819 a^{4} + 586 a^{3} + 3095 a^{2} + 134 a - 596\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-3a+1\right){x}^{2}+\left(89a^{4}-17a^{3}-439a^{2}-38a+86\right){x}-819a^{4}+586a^{3}+3095a^{2}+134a-596$ |
| 25.1-d4 |
25.1-d |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{4} \) |
$23.55381$ |
$(a^4-2a^3-2a^2+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$0.800796175$ |
$42.08738925$ |
1.76419015 |
\( \frac{488509962822731359638}{25} a^{4} - \frac{776547463172625188346}{25} a^{3} - \frac{1784205847864588683433}{25} a^{2} + \frac{342071130235394451034}{5} a + \frac{1190397818850374480652}{25} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 3\) , \( a^{2} - 1\) , \( 143 a^{4} - 101 a^{3} - 555 a^{2} + 8 a + 86\) , \( 747 a^{4} - 457 a^{3} - 2953 a^{2} - 247 a + 559\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-4a^{2}+6a+3\right){x}^{2}+\left(143a^{4}-101a^{3}-555a^{2}+8a+86\right){x}+747a^{4}-457a^{3}-2953a^{2}-247a+559$ |
| 27.1-a1 |
27.1-a |
$2$ |
$3$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$23.73578$ |
$(a^2-1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2129.057958$ |
1.23827296 |
\( -180015 a^{4} + 286223 a^{3} + 657933 a^{2} - 631336 a - 439430 \) |
\( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 6 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{2} + 3\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+3a^{2}-6a-1\right){x}^{2}+\left(-a^{2}+3\right){x}-1$ |
| 27.1-a2 |
27.1-a |
$2$ |
$3$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$23.73578$ |
$(a^2-1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$26.28466615$ |
1.23827296 |
\( 1418630703 a^{4} - 1053833686 a^{3} - 5351126785 a^{2} - 8280788 a + 937167631 \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{2} - a - 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( 374 a^{4} - 252 a^{3} - 1451 a^{2} - 59 a + 277\) , \( 5982 a^{4} - 3984 a^{3} - 23258 a^{2} - 1118 a + 4479\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(374a^{4}-252a^{3}-1451a^{2}-59a+277\right){x}+5982a^{4}-3984a^{3}-23258a^{2}-1118a+4479$ |
| 27.1-b1 |
27.1-b |
$2$ |
$3$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{5} \) |
$23.73578$ |
$(a^2-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 3 \) |
$0.001419619$ |
$16840.33282$ |
1.87709116 |
\( -180015 a^{4} + 286223 a^{3} + 657933 a^{2} - 631336 a - 439430 \) |
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 6 a + 1\) , \( -a^{4} + a^{3} + 3 a^{2} - a + 1\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -5 a^{4} + 6 a^{3} + 16 a^{2} - 9 a - 5\) , \( -3 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 3\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+6a+1\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(-a^{4}+a^{3}+3a^{2}-a+1\right){x}^{2}+\left(-5a^{4}+6a^{3}+16a^{2}-9a-5\right){x}-3a^{4}+3a^{3}+10a^{2}-5a-3$ |
| 27.1-b2 |
27.1-b |
$2$ |
$3$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{3} \) |
$23.73578$ |
$(a^2-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$0.004258859$ |
$16840.33282$ |
1.87709116 |
\( 1418630703 a^{4} - 1053833686 a^{3} - 5351126785 a^{2} - 8280788 a + 937167631 \) |
\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 8 a + 3\) , \( a^{3} - 5 a - 2\) , \( a^{4} - a^{3} - 3 a^{2} + a\) , \( -5 a^{3} + 2 a^{2} + 16 a - 1\) , \( 4 a^{4} - 4 a^{3} - 16 a^{2} + 6 a + 10\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-7a^{2}+8a+3\right){x}{y}+\left(a^{4}-a^{3}-3a^{2}+a\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(-5a^{3}+2a^{2}+16a-1\right){x}+4a^{4}-4a^{3}-16a^{2}+6a+10$ |
| 37.1-a1 |
37.1-a |
$2$ |
$3$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
37.1 |
\( 37 \) |
\( - 37^{3} \) |
$24.49556$ |
$(a^4-2a^3-2a^2+4a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 3 \) |
$1$ |
$10.08159607$ |
1.42483467 |
\( -\frac{1272945793794372}{50653} a^{4} + \frac{859591705080800}{50653} a^{3} + \frac{4922533480405137}{50653} a^{2} + \frac{233798144853843}{50653} a - \frac{948239678172729}{50653} \) |
\( \bigl[a\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( 32 a^{4} - 13 a^{3} - 148 a^{2} - 4 a + 30\) , \( 154 a^{4} - 69 a^{3} - 676 a^{2} - 48 a + 128\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){x}^{2}+\left(32a^{4}-13a^{3}-148a^{2}-4a+30\right){x}+154a^{4}-69a^{3}-676a^{2}-48a+128$ |
| 37.1-a2 |
37.1-a |
$2$ |
$3$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
37.1 |
\( 37 \) |
\( -37 \) |
$24.49556$ |
$(a^4-2a^3-2a^2+4a+1)$ |
$0$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$2449.827847$ |
1.42483467 |
\( \frac{434197}{37} a^{4} - \frac{726502}{37} a^{3} - \frac{1586537}{37} a^{2} + \frac{1678795}{37} a + \frac{1145975}{37} \) |
\( \bigl[a\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 6 a + 5\) , \( -a^{3} + 2 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){x}^{2}+\left(2a^{4}-3a^{3}-8a^{2}+6a+5\right){x}-a^{3}+2a-1$ |
| 37.1-b1 |
37.1-b |
$1$ |
$1$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
37.1 |
\( 37 \) |
\( -37 \) |
$24.49556$ |
$(a^4-2a^3-2a^2+4a+1)$ |
$0$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$288.0518460$ |
1.50779424 |
\( -\frac{12336731}{37} a^{4} - \frac{600304}{37} a^{3} + \frac{27788818}{37} a^{2} + \frac{2658172}{37} a - \frac{5310421}{37} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 8 a + 4\) , \( a^{2} - a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - a^{3} - a^{2} + a - 2\) , \( -4 a^{4} + 5 a^{3} + 15 a^{2} - 12 a - 11\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-7a^{2}+8a+4\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(a^{4}-a^{3}-a^{2}+a-2\right){x}-4a^{4}+5a^{3}+15a^{2}-12a-11$ |
| 37.1-c1 |
37.1-c |
$1$ |
$1$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
37.1 |
\( 37 \) |
\( -37 \) |
$24.49556$ |
$(a^4-2a^3-2a^2+4a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.002017156$ |
$31970.22748$ |
1.68782263 |
\( -\frac{12336731}{37} a^{4} - \frac{600304}{37} a^{3} + \frac{27788818}{37} a^{2} + \frac{2658172}{37} a - \frac{5310421}{37} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + a\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 8 a + 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 6 a - 5\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+a\right){x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+8a+3\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(a^{4}-2a^{3}-2a^{2}+4a-1\right){x}-2a^{4}+3a^{3}+7a^{2}-6a-5$ |
| 37.1-d1 |
37.1-d |
$2$ |
$3$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
37.1 |
\( 37 \) |
\( - 37^{3} \) |
$24.49556$ |
$(a^4-2a^3-2a^2+4a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.009869798$ |
$6342.573603$ |
1.63838223 |
\( -\frac{1272945793794372}{50653} a^{4} + \frac{859591705080800}{50653} a^{3} + \frac{4922533480405137}{50653} a^{2} + \frac{233798144853843}{50653} a - \frac{948239678172729}{50653} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( -a^{3} + 5 a + 2\) , \( a^{2} - 2\) , \( 7 a^{4} - 48 a^{3} - 16 a^{2} + 121 a - 21\) , \( -2 a^{4} + 130 a^{3} - 11 a^{2} - 300 a + 131\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(7a^{4}-48a^{3}-16a^{2}+121a-21\right){x}-2a^{4}+130a^{3}-11a^{2}-300a+131$ |
| 37.1-d2 |
37.1-d |
$2$ |
$3$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
37.1 |
\( 37 \) |
\( -37 \) |
$24.49556$ |
$(a^4-2a^3-2a^2+4a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.003289932$ |
$19027.72081$ |
1.63838223 |
\( \frac{434197}{37} a^{4} - \frac{726502}{37} a^{3} - \frac{1586537}{37} a^{2} + \frac{1678795}{37} a + \frac{1145975}{37} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( -a^{3} + 5 a + 2\) , \( a^{2} - 2\) , \( 2 a^{4} - 8 a^{3} - 6 a^{2} + 26 a + 14\) , \( -4 a^{3} + a^{2} + 17 a + 9\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(2a^{4}-8a^{3}-6a^{2}+26a+14\right){x}-4a^{3}+a^{2}+17a+9$ |
| 39.1-a1 |
39.1-a |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3 \cdot 13^{7} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$1$ |
\( 7 \) |
$1$ |
$416.4504504$ |
0.953702256 |
\( \frac{2355906526241759285697134}{188245551} a^{4} - \frac{2787719689830134456132135}{62748517} a^{3} + \frac{1984187604735214198024472}{62748517} a^{2} + \frac{2481423171042881641939612}{188245551} a - \frac{1509608417930564685187136}{188245551} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( -10 a^{4} - 442 a^{3} + 162 a^{2} + 997 a - 537\) , \( 1117 a^{4} + 6433 a^{3} - 3401 a^{2} - 13458 a + 5199\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-3\right){x}^{2}+\left(-10a^{4}-442a^{3}+162a^{2}+997a-537\right){x}+1117a^{4}+6433a^{3}-3401a^{2}-13458a+5199$ |
| 39.1-a2 |
39.1-a |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{28} \cdot 13^{4} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$4$ |
\( 2^{3} \) |
$1$ |
$22.77463401$ |
0.953702256 |
\( -\frac{245221713430759302881439941}{653384069306141121} a^{4} + \frac{54549846486679869070186093}{217794689768713707} a^{3} + \frac{317685914344297788746472133}{217794689768713707} a^{2} + \frac{44794650789260669643855797}{653384069306141121} a - \frac{183239072364466551195819934}{653384069306141121} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( 25 a^{4} - 77 a^{3} - 28 a^{2} + 177 a - 82\) , \( 195 a^{4} - 507 a^{3} - 353 a^{2} + 1180 a - 360\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-3\right){x}^{2}+\left(25a^{4}-77a^{3}-28a^{2}+177a-82\right){x}+195a^{4}-507a^{3}-353a^{2}+1180a-360$ |
| 39.1-a3 |
39.1-a |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{7} \cdot 13 \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$2915.153153$ |
0.953702256 |
\( -\frac{1065196}{28431} a^{4} + \frac{5295800}{9477} a^{3} + \frac{4095677}{9477} a^{2} - \frac{51097538}{28431} a + \frac{11953519}{28431} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 5 a + 3\) , \( 4 a^{4} - 3 a^{3} - 15 a^{2} + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+5a\right){x}^{2}+\left(a^{4}-2a^{3}-4a^{2}+5a+3\right){x}+4a^{4}-3a^{3}-15a^{2}+1$ |
| 39.1-a4 |
39.1-a |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{14} \cdot 13^{2} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2Cs, 7B.6.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$728.7882883$ |
0.953702256 |
\( \frac{681363632760910}{808321761} a^{4} - \frac{50134304890058}{269440587} a^{3} - \frac{518208005828660}{269440587} a^{2} + \frac{361111060198751}{808321761} a + \frac{518784067066631}{808321761} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( -5 a^{4} - 2 a^{3} + 22 a^{2} + 2 a - 17\) , \( 10 a^{4} - 36 a^{3} - 41 a^{2} + 75 a + 25\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-3\right){x}^{2}+\left(-5a^{4}-2a^{3}+22a^{2}+2a-17\right){x}+10a^{4}-36a^{3}-41a^{2}+75a+25$ |
| 39.1-a5 |
39.1-a |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{7} \cdot 13 \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.1 |
$4$ |
\( 1 \) |
$1$ |
$182.1970720$ |
0.953702256 |
\( \frac{250577525153856331}{28431} a^{4} + \frac{23688817181716957}{9477} a^{3} - \frac{188375931275690315}{9477} a^{2} - \frac{51297605922912091}{28431} a + \frac{111644917373722610}{28431} \) |
\( \bigl[a^{2} - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 1\) , \( 21 a^{4} + 48 a^{3} - 214 a^{2} - 40 a + 28\) , \( -319 a^{4} + 696 a^{3} + 155 a^{2} - 141 a + 20\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+6a+1\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+5a\right){x}^{2}+\left(21a^{4}+48a^{3}-214a^{2}-40a+28\right){x}-319a^{4}+696a^{3}+155a^{2}-141a+20$ |
| 39.1-a6 |
39.1-a |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{2} \cdot 13^{14} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2Cs, 7B.6.3 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$104.1126126$ |
0.953702256 |
\( -\frac{472782327302300801895731921547539}{35436387471293601} a^{4} + \frac{394975294976905362408499434574120}{11812129157097867} a^{3} + \frac{272811905305461777343354151432686}{11812129157097867} a^{2} - \frac{2778265732130705691487149505785760}{35436387471293601} a + \frac{933818725458499494056492136677657}{35436387471293601} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( 2185 a^{4} - 6512 a^{3} - 2423 a^{2} + 15352 a - 7692\) , \( -148316 a^{4} + 370555 a^{3} + 276975 a^{2} - 864563 a + 250675\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-3\right){x}^{2}+\left(2185a^{4}-6512a^{3}-2423a^{2}+15352a-7692\right){x}-148316a^{4}+370555a^{3}+276975a^{2}-864563a+250675$ |
| 39.1-a7 |
39.1-a |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{4} \cdot 13^{28} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$4$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$3.253519144$ |
0.953702256 |
\( \frac{719563077579420768826778357723754883977964219744702}{1255737557015654093436832343547201} a^{4} - \frac{381278393594661046595984821496687550631447920681206}{418579185671884697812277447849067} a^{3} - \frac{876030344833436911152144359572205314535143035049625}{418579185671884697812277447849067} a^{2} + \frac{2519311520172502928352178004640753313415969058351782}{1255737557015654093436832343547201} a + \frac{1753426510580954709523077468627597477978011837927249}{1255737557015654093436832343547201} \) |
\( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 7 a - 3\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( -8160 a^{4} + 9948 a^{3} + 35372 a^{2} - 20898 a - 32917\) , \( -915354 a^{4} + 1590551 a^{3} + 3078970 a^{2} - 3551457 a - 1619171\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-2a^{2}+4a\right){x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-7a-3\right){x}^{2}+\left(-8160a^{4}+9948a^{3}+35372a^{2}-20898a-32917\right){x}-915354a^{4}+1590551a^{3}+3078970a^{2}-3551457a-1619171$ |
| 39.1-a8 |
39.1-a |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3 \cdot 13^{7} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.6.3 |
$4$ |
\( 7 \) |
$1$ |
$26.02815315$ |
0.953702256 |
\( -\frac{167642752752633447006093524748799040238434}{188245551} a^{4} + \frac{140053631818257799009656597663946084463786}{62748517} a^{3} + \frac{96735383245269016352815198554224769104727}{62748517} a^{2} - \frac{985141440142117916445879153670063426054138}{188245551} a + \frac{331121807700898395019402938118329735513617}{188245551} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 3\) , \( -4706 a^{4} + 2553 a^{3} + 11325 a^{2} - 4556 a - 5334\) , \( 186623 a^{4} + 106339 a^{3} - 305029 a^{2} - 211344 a - 18618\bigr] \) |
${y}^2+{x}{y}+\left(2a^{4}-3a^{3}-7a^{2}+7a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-4706a^{4}+2553a^{3}+11325a^{2}-4556a-5334\right){x}+186623a^{4}+106339a^{3}-305029a^{2}-211344a-18618$ |
| 39.1-b1 |
39.1-b |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3 \cdot 13^{7} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 1 \) |
$1$ |
$0.477173882$ |
1.49927138 |
\( \frac{2355906526241759285697134}{188245551} a^{4} - \frac{2787719689830134456132135}{62748517} a^{3} + \frac{1984187604735214198024472}{62748517} a^{2} + \frac{2481423171042881641939612}{188245551} a - \frac{1509608417930564685187136}{188245551} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -324 a^{4} + 554 a^{3} + 1092 a^{2} - 1175 a - 803\) , \( -4619 a^{4} + 7541 a^{3} + 16214 a^{2} - 16147 a - 11168\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-324a^{4}+554a^{3}+1092a^{2}-1175a-803\right){x}-4619a^{4}+7541a^{3}+16214a^{2}-16147a-11168$ |
| 39.1-b2 |
39.1-b |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{28} \cdot 13^{4} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 2^{3} \cdot 7 \) |
$1$ |
$1002.482679$ |
1.49927138 |
\( -\frac{245221713430759302881439941}{653384069306141121} a^{4} + \frac{54549846486679869070186093}{217794689768713707} a^{3} + \frac{317685914344297788746472133}{217794689768713707} a^{2} + \frac{44794650789260669643855797}{653384069306141121} a - \frac{183239072364466551195819934}{653384069306141121} \) |
\( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 7 a - 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -4 a^{4} + 10 a^{3} - a^{2} + 8 a - 21\) , \( 38 a^{4} - 121 a^{3} + 60 a^{2} + 31 a + 19\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-3a^{2}+2a+1\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a\right){y}={x}^{3}+\left(-2a^{4}+3a^{3}+7a^{2}-7a-3\right){x}^{2}+\left(-4a^{4}+10a^{3}-a^{2}+8a-21\right){x}+38a^{4}-121a^{3}+60a^{2}+31a+19$ |
| 39.1-b3 |
39.1-b |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( - 3^{7} \cdot 13 \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$1$ |
\( 7 \) |
$1$ |
$8019.861435$ |
1.49927138 |
\( -\frac{1065196}{28431} a^{4} + \frac{5295800}{9477} a^{3} + \frac{4095677}{9477} a^{2} - \frac{51097538}{28431} a + \frac{11953519}{28431} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -4 a^{4} + 9 a^{3} + 12 a^{2} - 20 a - 3\) , \( 2 a^{4} - 9 a^{2} + 10\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-4a^{4}+9a^{3}+12a^{2}-20a-3\right){x}+2a^{4}-9a^{2}+10$ |
| 39.1-b4 |
39.1-b |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{14} \cdot 13^{2} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z\oplus\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2Cs, 7B.1.1 |
$1$ |
\( 2^{2} \cdot 7 \) |
$1$ |
$8019.861435$ |
1.49927138 |
\( \frac{681363632760910}{808321761} a^{4} - \frac{50134304890058}{269440587} a^{3} - \frac{518208005828660}{269440587} a^{2} + \frac{361111060198751}{808321761} a + \frac{518784067066631}{808321761} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 1\) , \( 8 a^{4} - 20 a^{3} - 18 a^{2} + 50 a - 15\) , \( -5 a^{4} + 14 a^{3} + 10 a^{2} - 35 a + 12\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(8a^{4}-20a^{3}-18a^{2}+50a-15\right){x}-5a^{4}+14a^{3}+10a^{2}-35a+12$ |
| 39.1-b5 |
39.1-b |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{7} \cdot 13 \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/14\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.1 |
$4$ |
\( 7 \) |
$1$ |
$2004.965358$ |
1.49927138 |
\( \frac{250577525153856331}{28431} a^{4} + \frac{23688817181716957}{9477} a^{3} - \frac{188375931275690315}{9477} a^{2} - \frac{51297605922912091}{28431} a + \frac{111644917373722610}{28431} \) |
\( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( 120 a^{4} - 100 a^{3} - 445 a^{2} + 30 a + 42\) , \( 665 a^{4} - 538 a^{3} - 2479 a^{2} + 223 a + 422\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-4a^{2}+2a+2\right){x}{y}+\left(a^{4}-2a^{3}-2a^{2}+4a\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+4a^{2}-5a-3\right){x}^{2}+\left(120a^{4}-100a^{3}-445a^{2}+30a+42\right){x}+665a^{4}-538a^{3}-2479a^{2}+223a+422$ |
| 39.1-b6 |
39.1-b |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{2} \cdot 13^{14} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2Cs, 7B.1.3 |
$2401$ |
\( 2^{2} \) |
$1$ |
$0.477173882$ |
1.49927138 |
\( -\frac{472782327302300801895731921547539}{35436387471293601} a^{4} + \frac{394975294976905362408499434574120}{11812129157097867} a^{3} + \frac{272811905305461777343354151432686}{11812129157097867} a^{2} - \frac{2778265732130705691487149505785760}{35436387471293601} a + \frac{933818725458499494056492136677657}{35436387471293601} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -4889 a^{4} + 8124 a^{3} + 17837 a^{2} - 18525 a - 13048\) , \( -269334 a^{4} + 434813 a^{3} + 983058 a^{2} - 970083 a - 674066\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-6a^{2}+7a+1\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-4889a^{4}+8124a^{3}+17837a^{2}-18525a-13048\right){x}-269334a^{4}+434813a^{3}+983058a^{2}-970083a-674066$ |
| 39.1-b7 |
39.1-b |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3^{4} \cdot 13^{28} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$2401$ |
\( 2^{3} \) |
$1$ |
$0.059646735$ |
1.49927138 |
\( \frac{719563077579420768826778357723754883977964219744702}{1255737557015654093436832343547201} a^{4} - \frac{381278393594661046595984821496687550631447920681206}{418579185671884697812277447849067} a^{3} - \frac{876030344833436911152144359572205314535143035049625}{418579185671884697812277447849067} a^{2} + \frac{2519311520172502928352178004640753313415969058351782}{1255737557015654093436832343547201} a + \frac{1753426510580954709523077468627597477978011837927249}{1255737557015654093436832343547201} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 1\) , \( 10238 a^{4} - 25455 a^{3} - 18068 a^{2} + 59680 a - 20375\) , \( 897162 a^{4} - 2245513 a^{3} - 1558277 a^{2} + 5265005 a - 1771850\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(10238a^{4}-25455a^{3}-18068a^{2}+59680a-20375\right){x}+897162a^{4}-2245513a^{3}-1558277a^{2}+5265005a-1771850$ |
| 39.1-b8 |
39.1-b |
$8$ |
$28$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
39.1 |
\( 3 \cdot 13 \) |
\( 3 \cdot 13^{7} \) |
$24.62485$ |
$(a^2-1), (a^3-3a)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 7$ |
2B, 7B.1.3 |
$9604$ |
\( 1 \) |
$1$ |
$0.119293470$ |
1.49927138 |
\( -\frac{167642752752633447006093524748799040238434}{188245551} a^{4} + \frac{140053631818257799009656597663946084463786}{62748517} a^{3} + \frac{96735383245269016352815198554224769104727}{62748517} a^{2} - \frac{985141440142117916445879153670063426054138}{188245551} a + \frac{331121807700898395019402938118329735513617}{188245551} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( 22858 a^{4} - 15206 a^{3} - 89524 a^{2} - 4349 a + 16767\) , \( 2975973 a^{4} - 1981540 a^{3} - 11583514 a^{2} - 559230 a + 2228472\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+5a+2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+2a^{2}-5a\right){x}^{2}+\left(22858a^{4}-15206a^{3}-89524a^{2}-4349a+16767\right){x}+2975973a^{4}-1981540a^{3}-11583514a^{2}-559230a+2228472$ |
| 49.1-a1 |
49.1-a |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{8} \) |
$25.19340$ |
$(a^4-2a^3-4a^2+6a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.065885382$ |
$2381.844613$ |
2.05359085 |
\( \frac{19567537797912176446}{2401} a^{4} - \frac{69587777857668838427}{2401} a^{3} + \frac{49595930261394340581}{2401} a^{2} + \frac{20652200646025945743}{2401} a - \frac{12573218933743386648}{2401} \) |
\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 7 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( a^{2} - 2\) , \( -127 a^{4} + 191 a^{3} + 470 a^{2} - 400 a - 351\) , \( -1617 a^{4} + 2597 a^{3} + 5876 a^{2} - 5786 a - 3783\bigr] \) |
${y}^2+\left(2a^{4}-3a^{3}-7a^{2}+7a+4\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){x}^{2}+\left(-127a^{4}+191a^{3}+470a^{2}-400a-351\right){x}-1617a^{4}+2597a^{3}+5876a^{2}-5786a-3783$ |
| 49.1-a2 |
49.1-a |
$4$ |
$4$ |
5.5.36497.1 |
$5$ |
$[5, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{2} \) |
$25.19340$ |
$(a^4-2a^3-4a^2+6a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.016471345$ |
$19054.75690$ |
2.05359085 |
\( \frac{827}{7} a^{4} + 5033 a^{3} - \frac{28282}{7} a^{2} - \frac{26855}{7} a + \frac{13946}{7} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 6 a + 2\) , \( 2 a^{4} - 3 a^{3} - 8 a^{2} + 9 a + 5\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( 10 a^{4} - 17 a^{3} - 35 a^{2} + 39 a + 24\) , \( 16 a^{4} - 27 a^{3} - 54 a^{2} + 56 a + 36\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+6a+2\right){x}{y}+\left(2a^{4}-3a^{3}-6a^{2}+7a+2\right){y}={x}^{3}+\left(2a^{4}-3a^{3}-8a^{2}+9a+5\right){x}^{2}+\left(10a^{4}-17a^{3}-35a^{2}+39a+24\right){x}+16a^{4}-27a^{3}-54a^{2}+56a+36$ |
*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.
