| 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 |
| 2.1-a1 |
2.1-a |
$1$ |
$1$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
2.1 |
\( 2 \) |
\( 2^{7} \) |
$12.86445$ |
$(a^3+a^2-3a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$0.001617366$ |
$3580.167477$ |
1.228135084 |
\( \frac{217055}{8} a^{3} - \frac{66555}{8} a^{2} - \frac{209753}{2} a - \frac{135953}{2} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{2} + a + 4\) , \( a\) , \( 70 a^{3} + 45 a^{2} - 338 a - 258\) , \( -378 a^{3} - 178 a^{2} + 2026 a + 1522\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(70a^{3}+45a^{2}-338a-258\right){x}-378a^{3}-178a^{2}+2026a+1522$ |
| 3.1-a1 |
3.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$13.53326$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1318.018622$ |
1.247980455 |
\( \frac{6532552}{729} a^{3} + \frac{106419908}{729} a^{2} - \frac{10237156}{81} a - \frac{129173063}{729} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -2 a^{3} + 6 a^{2} + 8 a - 25\) , \( -a^{3} - 9 a^{2} - 2 a + 25\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-2a^{3}+6a^{2}+8a-25\right){x}-a^{3}-9a^{2}-2a+25$ |
| 3.1-a2 |
3.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$13.53326$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$164.7523278$ |
1.247980455 |
\( -\frac{54347563354}{27} a^{3} + \frac{2324909261368}{27} a^{2} - \frac{180204994382}{3} a - \frac{2746685896783}{27} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -12 a^{3} - 34 a^{2} + 18 a + 80\) , \( -151 a^{3} - 333 a^{2} + 340 a + 781\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-12a^{3}-34a^{2}+18a+80\right){x}-151a^{3}-333a^{2}+340a+781$ |
| 3.1-a3 |
3.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{12} \) |
$13.53326$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1318.018622$ |
1.247980455 |
\( \frac{3337036595986}{531441} a^{3} - \frac{5992561643896}{531441} a^{2} - \frac{1701775565758}{59049} a + \frac{25553485816549}{531441} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{2} - a + 2\) , \( 1\) , \( 16 a^{3} - 49 a^{2} + 9 a + 44\) , \( -28 a^{3} + 88 a^{2} - 16 a - 81\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(16a^{3}-49a^{2}+9a+44\right){x}-28a^{3}+88a^{2}-16a-81$ |
| 3.1-a4 |
3.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{6} \) |
$13.53326$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$329.5046556$ |
1.247980455 |
\( \frac{278913184719367931}{729} a^{3} - \frac{498621852085325861}{729} a^{2} - \frac{142301382327925598}{81} a + \frac{2124513622724029835}{729} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{2} - a + 2\) , \( 1\) , \( 151 a^{3} - 464 a^{2} + 89 a + 389\) , \( 3325 a^{3} - 10335 a^{2} + 1800 a + 9537\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+{y}={x}^{3}+\left(-a^{2}-a+2\right){x}^{2}+\left(151a^{3}-464a^{2}+89a+389\right){x}+3325a^{3}-10335a^{2}+1800a+9537$ |
| 3.1-a5 |
3.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$13.53326$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$659.0093112$ |
1.247980455 |
\( \frac{14548}{27} a^{3} - \frac{42472}{27} a^{2} - \frac{6880}{3} a + \frac{186739}{27} \) |
\( \bigl[1\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -2 a^{3} + 3 a^{2} + 9 a - 11\) , \( -3 a^{3} + a^{2} + 11 a - 9\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-2a^{3}+3a^{2}+9a-11\right){x}-3a^{3}+a^{2}+11a-9$ |
| 3.1-a6 |
3.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{24} \) |
$13.53326$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$329.5046556$ |
1.247980455 |
\( \frac{4097874321591589}{282429536481} a^{3} + \frac{6358144207494701}{282429536481} a^{2} - \frac{1221753416465122}{31381059609} a - \frac{12601406735198051}{282429536481} \) |
\( \bigl[1\) , \( -a^{3} + 4 a + 1\) , \( a\) , \( -128 a^{3} - 174 a^{2} + 354 a + 324\) , \( 2008 a^{3} + 2748 a^{2} - 5538 a - 5085\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-128a^{3}-174a^{2}+354a+324\right){x}+2008a^{3}+2748a^{2}-5538a-5085$ |
| 4.2-a1 |
4.2-a |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{5} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$285.0836219$ |
1.079738274 |
\( -\frac{2777}{8} a^{3} - 256 a^{2} + \frac{6283}{4} a + \frac{4775}{4} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} + 4 a + 2\) , \( a^{2} - 3\) , \( -2 a^{2} + 8 a + 8\) , \( 31 a^{3} - 95 a^{2} + 22 a + 90\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-2a^{2}+8a+8\right){x}+31a^{3}-95a^{2}+22a+90$ |
| 4.2-a2 |
4.2-a |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{7} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$285.0836219$ |
1.079738274 |
\( -\frac{203781283}{4} a^{3} - 9421095 a^{2} + \frac{520432299}{2} a + \frac{454100027}{4} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 4\) , \( 1\) , \( a^{3} + 2 a^{2} - 3 a - 2\) , \( 2 a^{3} + 5 a^{2} - 7 a - 8\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(a^{3}+2a^{2}-3a-2\right){x}+2a^{3}+5a^{2}-7a-8$ |
| 4.2-a3 |
4.2-a |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{5} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$285.0836219$ |
1.079738274 |
\( \frac{2175674505972627}{4} a^{3} - 972369092711197 a^{2} - \frac{4995132640043851}{2} a + 4143033963999329 \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 5 a - 5\) , \( a^{2} - 2\) , \( 112 a^{3} - 299 a^{2} - 16 a + 227\) , \( -1762 a^{3} + 5119 a^{2} - 402 a - 4355\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-5\right){x}^{2}+\left(112a^{3}-299a^{2}-16a+227\right){x}-1762a^{3}+5119a^{2}-402a-4355$ |
| 4.2-a4 |
4.2-a |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{7} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$285.0836219$ |
1.079738274 |
\( \frac{17786017}{64} a^{3} + \frac{5508859}{16} a^{2} - \frac{26065429}{32} a - \frac{17439407}{32} \) |
\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -20 a^{3} - 27 a^{2} + 54 a + 51\) , \( -111 a^{3} - 152 a^{2} + 306 a + 281\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a^{3}-27a^{2}+54a+51\right){x}-111a^{3}-152a^{2}+306a+281$ |
| 4.2-b1 |
4.2-b |
$2$ |
$3$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{9} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 7 \) |
$0.005569617$ |
$1006.513634$ |
2.377985903 |
\( -\frac{190634171}{128} a^{3} + \frac{85198175}{32} a^{2} + \frac{437664823}{64} a - \frac{725957579}{64} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -1\) , \( a^{2} - 2\) , \( -6 a^{3} + 15 a^{2} + 30 a - 58\) , \( 28 a^{3} - 43 a^{2} - 124 a + 190\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}-{x}^{2}+\left(-6a^{3}+15a^{2}+30a-58\right){x}+28a^{3}-43a^{2}-124a+190$ |
| 4.2-b2 |
4.2-b |
$2$ |
$3$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( 2^{27} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \cdot 7 \) |
$0.001856539$ |
$1006.513634$ |
2.377985903 |
\( -\frac{7242419331}{2097152} a^{3} - \frac{16739289881}{524288} a^{2} - \frac{36498921601}{1048576} a - \frac{9747477587}{1048576} \) |
\( \bigl[a^{2} + a - 3\) , \( a - 1\) , \( a^{2} + a - 2\) , \( -116 a^{3} - 157 a^{2} + 320 a + 289\) , \( 1374 a^{3} + 1868 a^{2} - 3797 a - 3441\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-116a^{3}-157a^{2}+320a+289\right){x}+1374a^{3}+1868a^{2}-3797a-3441$ |
| 4.2-c1 |
4.2-c |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{63} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$8.640591466$ |
0.294531812 |
\( -\frac{10495049249}{2097152} a^{3} - \frac{520166291}{524288} a^{2} + \frac{27328674037}{1048576} a + \frac{10950681647}{1048576} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 4 a\) , \( 125 a^{3} + 180 a^{2} - 346 a - 357\) , \( 7601 a^{3} + 10450 a^{2} - 20942 a - 19415\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(125a^{3}+180a^{2}-346a-357\right){x}+7601a^{3}+10450a^{2}-20942a-19415$ |
| 4.2-c2 |
4.2-c |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{21} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$699.8879087$ |
0.294531812 |
\( -\frac{14709465}{128} a^{3} - 145632 a^{2} + \frac{22472843}{64} a + \frac{19999271}{64} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 4 a\) , \( -115 a^{3} - 160 a^{2} + 314 a + 298\) , \( 1398 a^{3} + 1912 a^{2} - 3856 a - 3536\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+1\right){x}^{2}+\left(-115a^{3}-160a^{2}+314a+298\right){x}+1398a^{3}+1912a^{2}-3856a-3536$ |
| 4.2-c3 |
4.2-c |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{21} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$699.8879087$ |
0.294531812 |
\( \frac{1984846635054593}{16384} a^{3} + \frac{679139774982963}{4096} a^{2} - \frac{2737251907868245}{8192} a - \frac{2513896718002703}{8192} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{3} - 3 a - 1\) , \( 12 a^{3} + 2 a^{2} - 64 a - 32\) , \( -746 a^{3} - 395 a^{2} + 3877 a + 2940\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(12a^{3}+2a^{2}-64a-32\right){x}-746a^{3}-395a^{2}+3877a+2940$ |
| 4.2-c4 |
4.2-c |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{63} \) |
$14.02878$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$8.640591466$ |
0.294531812 |
\( \frac{35263376290057077889}{4398046511104} a^{3} - \frac{15250659102442875725}{1099511627776} a^{2} - \frac{84898703459479142101}{2199023255552} a + \frac{137936503947327491185}{2199023255552} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{3} - 3 a - 1\) , \( -118 a^{3} - 38 a^{2} + 606 a + 333\) , \( 20036 a^{3} + 10735 a^{2} - 104175 a - 79746\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-118a^{3}-38a^{2}+606a+333\right){x}+20036a^{3}+10735a^{2}-104175a-79746$ |
| 6.1-a1 |
6.1-a |
$2$ |
$3$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{3} \cdot 3^{12} \) |
$14.75813$ |
$(a^3+a^2-3a-2), (a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.066733506$ |
$252.6170166$ |
3.064742644 |
\( -\frac{160594220419}{531441} a^{3} + \frac{90314696560}{531441} a^{2} + \frac{332293716521}{118098} a - \frac{3843194899295}{1062882} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 2\) , \( -7 a^{3} + 8 a^{2} + 39 a - 50\) , \( -23 a^{3} + 43 a^{2} + 96 a - 166\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-7a^{3}+8a^{2}+39a-50\right){x}-23a^{3}+43a^{2}+96a-166$ |
| 6.1-a2 |
6.1-a |
$2$ |
$3$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{9} \cdot 3^{4} \) |
$14.75813$ |
$(a^3+a^2-3a-2), (a^2-a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.022244502$ |
$252.6170166$ |
3.064742644 |
\( \frac{93661}{648} a^{3} + \frac{128039}{648} a^{2} - \frac{28705}{72} a - \frac{234827}{648} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 14 a^{3} + 18 a^{2} - 42 a - 33\) , \( 9 a^{3} + 11 a^{2} - 26 a - 21\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(14a^{3}+18a^{2}-42a-33\right){x}+9a^{3}+11a^{2}-26a-21$ |
| 6.2-a1 |
6.2-a |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{7} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 7 \) |
$0.016815231$ |
$1525.046500$ |
1.359753572 |
\( -\frac{896303587109}{4374} a^{3} - \frac{235926736574}{2187} a^{2} + \frac{258786405697}{243} a + \frac{1762526925611}{2187} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 9 a^{3} + 12 a^{2} - 20 a - 18\) , \( 69 a^{3} + 96 a^{2} - 188 a - 174\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(9a^{3}+12a^{2}-20a-18\right){x}+69a^{3}+96a^{2}-188a-174$ |
| 6.2-a2 |
6.2-a |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{14} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 7 \) |
$0.008407615$ |
$762.5232502$ |
1.359753572 |
\( \frac{105876153145}{19131876} a^{3} + \frac{16093877243}{4782969} a^{2} - \frac{30049895429}{1062882} a - \frac{207785542903}{9565938} \) |
\( \bigl[a\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 4 a - 1\) , \( -31 a^{3} - 42 a^{2} + 88 a + 81\) , \( 129 a^{3} + 176 a^{2} - 357 a - 328\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(-31a^{3}-42a^{2}+88a+81\right){x}+129a^{3}+176a^{2}-357a-328$ |
| 6.2-b1 |
6.2-b |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{9} \cdot 3^{3} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3^{2} \) |
$0.047831803$ |
$929.1600726$ |
3.029884165 |
\( -\frac{153602966573525}{13824} a^{3} + \frac{119314776774545}{3456} a^{2} - \frac{4667400758735}{768} a - \frac{218693664752773}{6912} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 3 a - 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 10 a^{3} - 26 a - 40\) , \( -31 a^{3} + 54 a^{2} + 76 a - 26\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-4\right){x}^{2}+\left(10a^{3}-26a-40\right){x}-31a^{3}+54a^{2}+76a-26$ |
| 6.2-b2 |
6.2-b |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3 \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.143495409$ |
$929.1600726$ |
3.029884165 |
\( \frac{4397683}{24} a^{3} - \frac{2350615}{6} a^{2} - \frac{3304805}{4} a + \frac{20636483}{12} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 1\) , \( 107 a^{3} + 57 a^{2} - 556 a - 414\) , \( 1124 a^{3} + 590 a^{2} - 5838 a - 4411\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(107a^{3}+57a^{2}-556a-414\right){x}+1124a^{3}+590a^{2}-5838a-4411$ |
| 6.2-b3 |
6.2-b |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{2} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.071747704$ |
$464.5800363$ |
3.029884165 |
\( \frac{24574057}{576} a^{3} + \frac{8454635}{144} a^{2} - \frac{3762485}{32} a - \frac{31393831}{288} \) |
\( \bigl[a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 1\) , \( -3 a^{3} - 4 a^{2} + 6 a + 10\) , \( -13 a^{3} - 19 a^{2} + 36 a + 35\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-3a^{3}-4a^{2}+6a+10\right){x}-13a^{3}-19a^{2}+36a+35$ |
| 6.2-b4 |
6.2-b |
$4$ |
$6$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{18} \cdot 3^{6} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.023915901$ |
$464.5800363$ |
3.029884165 |
\( \frac{4497505605241}{191102976} a^{3} - \frac{3329140969189}{47775744} a^{2} + \frac{107100535291}{10616832} a + \frac{6047657737961}{95551488} \) |
\( \bigl[a\) , \( -a^{3} - a^{2} + 3 a + 5\) , \( a^{3} - 4 a - 1\) , \( 9 a^{3} - 28 a^{2} + 2 a + 39\) , \( -32 a^{3} + 95 a^{2} - 9 a - 94\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+5\right){x}^{2}+\left(9a^{3}-28a^{2}+2a+39\right){x}-32a^{3}+95a^{2}-9a-94$ |
| 6.2-c1 |
6.2-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{40} \cdot 3 \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.819904100$ |
$244.1857678$ |
3.033120234 |
\( \frac{1941489375044231555}{3298534883328} a^{3} - \frac{903238929192764903}{824633720832} a^{2} - \frac{1502482670111443669}{549755813888} a + \frac{7636118509425768787}{1649267441664} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 3 a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -141 a^{3} - 191 a^{2} + 387 a + 352\) , \( 1639 a^{3} + 2242 a^{2} - 4520 a - 4149\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-3a-2\right){x}^{2}+\left(-141a^{3}-191a^{2}+387a+352\right){x}+1639a^{3}+2242a^{2}-4520a-4149$ |
| 6.2-c2 |
6.2-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{5} \cdot 3^{2} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.409952050$ |
$488.3715356$ |
3.033120234 |
\( -\frac{757396097}{288} a^{3} - \frac{99657139}{72} a^{2} + \frac{218687341}{16} a + \frac{1488940319}{144} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} + a - 2\) , \( 22 a^{3} + 12 a^{2} - 113 a - 81\) , \( 93 a^{3} + 52 a^{2} - 479 a - 370\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+1\right){x}^{2}+\left(22a^{3}+12a^{2}-113a-81\right){x}+93a^{3}+52a^{2}-479a-370$ |
| 6.2-c3 |
6.2-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.204976025$ |
$976.7430712$ |
3.033120234 |
\( -\frac{35621509631}{82944} a^{3} + \frac{29002092851}{20736} a^{2} - \frac{1342719725}{4608} a - \frac{53135067151}{41472} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{3} - 3 a - 1\) , \( -31 a^{3} - 49 a^{2} + 84 a + 97\) , \( 215 a^{3} + 291 a^{2} - 595 a - 535\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{2}-a+4\right){x}^{2}+\left(-31a^{3}-49a^{2}+84a+97\right){x}+215a^{3}+291a^{2}-595a-535$ |
| 6.2-c4 |
6.2-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( - 2^{5} \cdot 3^{8} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.409952050$ |
$122.0928839$ |
3.033120234 |
\( -\frac{894228620989257127}{209952} a^{3} + \frac{694618225140901243}{52488} a^{2} - \frac{27176185305514981}{11664} a - \frac{1273133894469232583}{104976} \) |
\( \bigl[1\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -47 a^{3} + 64 a^{2} + 214 a - 268\) , \( -250 a^{3} + 498 a^{2} + 1130 a - 2167\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-47a^{3}+64a^{2}+214a-268\right){x}-250a^{3}+498a^{2}+1130a-2167$ |
| 6.2-c5 |
6.2-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3 \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.819904100$ |
$244.1857678$ |
3.033120234 |
\( \frac{203577359955865513217005}{3072} a^{3} + \frac{69656506458528666355511}{768} a^{2} - \frac{93582799775291643244347}{512} a - \frac{257839799809998536520931}{1536} \) |
\( \bigl[1\) , \( a^{3} - 4 a\) , \( a^{2} - 3\) , \( a^{3} + 119 a^{2} - 195 a - 222\) , \( -640 a^{3} + 1155 a^{2} + 967 a - 267\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(a^{3}+119a^{2}-195a-222\right){x}-640a^{3}+1155a^{2}+967a-267$ |
| 6.2-c6 |
6.2-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
6.2 |
\( 2 \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$14.75813$ |
$(-a^2+2a+1), (a^2-a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.409952050$ |
$976.7430712$ |
3.033120234 |
\( \frac{22268319854463145}{9437184} a^{3} + \frac{7619383631741099}{2359296} a^{2} - \frac{3412184680004725}{524288} a - \frac{28203795751907815}{4718592} \) |
\( \bigl[1\) , \( a^{3} - 4 a\) , \( a^{2} - 3\) , \( 16 a^{3} - 41 a^{2} - 5 a + 33\) , \( -73 a^{3} + 210 a^{2} - 13 a - 177\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(16a^{3}-41a^{2}-5a+33\right){x}-73a^{3}+210a^{2}-13a-177$ |
| 8.3-a1 |
8.3-a |
$2$ |
$3$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{11} \) |
$15.29849$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.163226853$ |
$648.2468780$ |
3.206034989 |
\( -\frac{1971}{2} a^{3} + \frac{1517}{2} a^{2} + \frac{8813}{2} a - \frac{7247}{2} \) |
\( \bigl[a^{2} - 3\) , \( -a^{3} + 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -7 a^{3} - 7 a^{2} + 25 a + 20\) , \( 6 a^{3} + 10 a^{2} - 11 a - 12\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(-7a^{3}-7a^{2}+25a+20\right){x}+6a^{3}+10a^{2}-11a-12$ |
| 8.3-a2 |
8.3-a |
$2$ |
$3$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
8.3 |
\( 2^{3} \) |
\( 2^{17} \) |
$15.29849$ |
$(a^3+a^2-3a-2), (-a^2+2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.054408951$ |
$648.2468780$ |
3.206034989 |
\( -\frac{6623193813}{4} a^{3} - \frac{9064833529}{4} a^{2} + \frac{36535505751}{8} a + \frac{33554288521}{8} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 4\) , \( a + 1\) , \( -a^{3} - 5 a^{2} + 5 a + 25\) , \( -3 a^{2} + 14\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-a^{3}-5a^{2}+5a+25\right){x}-3a^{2}+14$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{3} \) |
$15.52539$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$866.0958222$ |
3.280289489 |
\( 5190839 a^{3} + 7103956 a^{2} - 14315910 a - 13147506 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 4 a\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - 11 a^{2} + 7 a + 15\) , \( 9 a^{3} - 36 a^{2} + 11 a + 37\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(a^{3}-11a^{2}+7a+15\right){x}+9a^{3}-36a^{2}+11a+37$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{3} \) |
$15.52539$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$866.0958222$ |
3.280289489 |
\( -751151 a^{3} + 2332108 a^{2} - 414058 a - 2128398 \) |
\( \bigl[a\) , \( a^{3} - 3 a\) , \( 1\) , \( -14 a^{3} + 30 a^{2} + 67 a - 123\) , \( 60 a^{3} - 103 a^{2} - 273 a + 443\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{3}-3a\right){x}^{2}+\left(-14a^{3}+30a^{2}+67a-123\right){x}+60a^{3}-103a^{2}-273a+443$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{3} \) |
$15.52539$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$96.49308126$ |
0.365462148 |
\( -14286680089 a^{3} - 7516966892 a^{2} + 74247864474 a + 56166863598 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - 4 a - 1\) , \( -5 a^{3} + 16 a^{2} + 18 a - 54\) , \( -32 a^{3} + 62 a^{2} + 150 a - 266\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(-5a^{3}+16a^{2}+18a-54\right){x}-32a^{3}+62a^{2}+150a-266$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{3} \) |
$15.52539$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$96.49308126$ |
0.365462148 |
\( 11017274481 a^{3} - 19695594228 a^{2} - 50589164138 a + 83918179122 \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a^{3} - 4 a - 1\) , \( -14 a^{3} + 8 a^{2} + 120 a - 144\) , \( -131 a^{3} + 274 a^{2} + 446 a - 854\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-3\right){x}^{2}+\left(-14a^{3}+8a^{2}+120a-144\right){x}-131a^{3}+274a^{2}+446a-854$ |
| 9.1-c1 |
9.1-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{30} \) |
$15.52539$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.564933523$ |
$48.68169988$ |
2.308329726 |
\( \frac{4097874321591589}{282429536481} a^{3} + \frac{6358144207494701}{282429536481} a^{2} - \frac{1221753416465122}{31381059609} a - \frac{12601406735198051}{282429536481} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} + 5 a\) , \( a^{3} - 4 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a - 12\) , \( 12 a^{3} - 12 a^{2} - 70 a + 17\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-2a^{3}+3a^{2}+9a-12\right){x}+12a^{3}-12a^{2}-70a+17$ |
| 9.1-c2 |
9.1-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{12} \) |
$15.52539$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.564933523$ |
$97.36339976$ |
2.308329726 |
\( \frac{278913184719367931}{729} a^{3} - \frac{498621852085325861}{729} a^{2} - \frac{142301382327925598}{81} a + \frac{2124513622724029835}{729} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} + a - 2\) , \( 1775 a^{3} + 996 a^{2} - 9041 a - 6861\) , \( 71963 a^{3} + 38168 a^{2} - 373103 a - 282398\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(1775a^{3}+996a^{2}-9041a-6861\right){x}+71963a^{3}+38168a^{2}-373103a-282398$ |
| 9.1-c3 |
9.1-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{18} \) |
$15.52539$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.782466761$ |
$389.4535990$ |
2.308329726 |
\( \frac{3337036595986}{531441} a^{3} - \frac{5992561643896}{531441} a^{2} - \frac{1701775565758}{59049} a + \frac{25553485816549}{531441} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{2} + a - 2\) , \( 90 a^{3} + 31 a^{2} - 511 a - 366\) , \( 1068 a^{3} + 522 a^{2} - 5656 a - 4247\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+3\right){x}^{2}+\left(90a^{3}+31a^{2}-511a-366\right){x}+1068a^{3}+522a^{2}-5656a-4247$ |
| 9.1-c4 |
9.1-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{12} \) |
$15.52539$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.391233380$ |
$778.9071981$ |
2.308329726 |
\( \frac{6532552}{729} a^{3} + \frac{106419908}{729} a^{2} - \frac{10237156}{81} a - \frac{129173063}{729} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 3 a - 4\) , \( -4 a^{3} - a^{2} + 16 a - 3\) , \( -3 a^{2} - a + 8\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(-4a^{3}-a^{2}+16a-3\right){x}-3a^{2}-a+8$ |
| 9.1-c5 |
9.1-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$15.52539$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.782466761$ |
$194.7267995$ |
2.308329726 |
\( -\frac{54347563354}{27} a^{3} + \frac{2324909261368}{27} a^{2} - \frac{180204994382}{3} a - \frac{2746685896783}{27} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 3 a - 4\) , \( -4 a^{3} - 21 a^{2} + 16 a + 42\) , \( 35 a^{3} - 10 a^{2} - 98 a + 47\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(-4a^{3}-21a^{2}+16a+42\right){x}+35a^{3}-10a^{2}-98a+47$ |
| 9.1-c6 |
9.1-c |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$15.52539$ |
$(a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.195616690$ |
$389.4535990$ |
2.308329726 |
\( \frac{14548}{27} a^{3} - \frac{42472}{27} a^{2} - \frac{6880}{3} a + \frac{186739}{27} \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 0\) , \( -3 a^{3} - a^{2} + 7 a + 6\) , \( 12 a^{3} + 19 a^{2} - 34 a - 33\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-3a^{3}-a^{2}+7a+6\right){x}+12a^{3}+19a^{2}-34a-33$ |
| 9.1-d1 |
9.1-d |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$15.52539$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$517.0891800$ |
1.958446350 |
\( 5190839 a^{3} + 7103956 a^{2} - 14315910 a - 13147506 \) |
\( \bigl[a^{3} - 4 a\) , \( a^{2} + a - 3\) , \( a^{3} - 3 a - 1\) , \( 5 a^{3} - 5 a^{2} - 15 a + 12\) , \( 11 a^{3} - 11 a^{2} - 61 a + 77\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(5a^{3}-5a^{2}-15a+12\right){x}+11a^{3}-11a^{2}-61a+77$ |
| 9.1-d2 |
9.1-d |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$15.52539$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$517.0891800$ |
1.958446350 |
\( -751151 a^{3} + 2332108 a^{2} - 414058 a - 2128398 \) |
\( \bigl[a\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{2} + a - 3\) , \( -417 a^{3} - 570 a^{2} + 1152 a + 1056\) , \( -11884 a^{3} - 16264 a^{2} + 32779 a + 30101\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(-417a^{3}-570a^{2}+1152a+1056\right){x}-11884a^{3}-16264a^{2}+32779a+30101$ |
| 9.1-e1 |
9.1-e |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$15.52539$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$227.9784583$ |
0.863455661 |
\( 11017274481 a^{3} - 19695594228 a^{2} - 50589164138 a + 83918179122 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 107 a^{3} + 149 a^{2} - 292 a - 270\) , \( 1713 a^{3} + 2346 a^{2} - 4722 a - 4338\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-1\right){x}^{2}+\left(107a^{3}+149a^{2}-292a-270\right){x}+1713a^{3}+2346a^{2}-4722a-4338$ |
| 9.1-e2 |
9.1-e |
$2$ |
$2$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$15.52539$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$227.9784583$ |
0.863455661 |
\( -14286680089 a^{3} - 7516966892 a^{2} + 74247864474 a + 56166863598 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 1\) , \( -79 a^{3} - 106 a^{2} + 216 a + 198\) , \( 554 a^{3} + 760 a^{2} - 1529 a - 1406\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-79a^{3}-106a^{2}+216a+198\right){x}+554a^{3}+760a^{2}-1529a-1406$ |
| 12.1-a1 |
12.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{16} \) |
$16.09385$ |
$(a^3+a^2-3a-2), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.131776321$ |
$292.1310556$ |
1.749615359 |
\( -\frac{46790270703425}{43046721} a^{3} - \frac{24652913278000}{43046721} a^{2} + \frac{27018038442794}{4782969} a + \frac{184160009581822}{43046721} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 4 a\) , \( 10 a^{3} + 16 a^{2} - 31 a - 27\) , \( -41 a^{3} - 56 a^{2} + 113 a + 102\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-4\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(10a^{3}+16a^{2}-31a-27\right){x}-41a^{3}-56a^{2}+113a+102$ |
| 12.1-a2 |
12.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$16.09385$ |
$(a^3+a^2-3a-2), (a^2-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.131776321$ |
$292.1310556$ |
1.749615359 |
\( \frac{2989301429}{81} a^{3} + \frac{4101873916}{81} a^{2} - \frac{916968866}{9} a - \frac{7584848182}{81} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 4\) , \( 17 a^{3} - 62 a^{2} + 20 a + 63\) , \( -146 a^{3} + 446 a^{2} - 72 a - 406\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-3a-4\right){y}={x}^{3}+\left(-a^{3}+5a+1\right){x}^{2}+\left(17a^{3}-62a^{2}+20a+63\right){x}-146a^{3}+446a^{2}-72a-406$ |
| 12.1-a3 |
12.1-a |
$6$ |
$8$ |
4.4.17428.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$16.09385$ |
$(a^3+a^2-3a-2), (a^2-a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.263552642$ |
$584.2621112$ |
1.749615359 |
\( \frac{18959209}{6561} a^{3} - \frac{3068788}{6561} a^{2} - \frac{7327498}{729} a + \frac{63972658}{6561} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -5 a^{3} + 5 a^{2} + 22 a - 22\) , \( -9 a^{3} + 15 a^{2} + 40 a - 67\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-4a-4\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+4\right){x}^{2}+\left(-5a^{3}+5a^{2}+22a-22\right){x}-9a^{3}+15a^{2}+40a-67$ |
*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.
