| 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 |
$2$ |
$2$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.33038$ |
$(a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$79.01005269$ |
2.351448007 |
\( \frac{841510}{729} a^{2} - \frac{114433}{729} a - \frac{1729327}{243} \) |
\( \bigl[a^{2} - a - 5\) , \( a\) , \( a^{2} - a - 5\) , \( a - 3\) , \( -2\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+a{x}^{2}+\left(a-3\right){x}-2$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{13} \) |
$4.33038$ |
$(a), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$39.50502634$ |
2.351448007 |
\( -\frac{4693612176319}{531441} a^{2} + \frac{2037168538759}{531441} a + \frac{10678157576125}{177147} \) |
\( \bigl[a^{2} - a - 5\) , \( a\) , \( a^{2} - a - 5\) , \( 6 a - 3\) , \( 3 a^{2} - 2 a - 8\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+a{x}^{2}+\left(6a-3\right){x}+3a^{2}-2a-8$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{13} \) |
$4.33038$ |
$(a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.168625337$ |
$55.72676915$ |
2.516994322 |
\( -\frac{4693612176319}{531441} a^{2} + \frac{2037168538759}{531441} a + \frac{10678157576125}{177147} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a + 1\) , \( 14 a^{2} + 5 a - 131\) , \( -80 a^{2} + 72 a + 437\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(14a^{2}+5a-131\right){x}-80a^{2}+72a+437$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.33038$ |
$(a), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.084312668$ |
$111.4535383$ |
2.516994322 |
\( \frac{841510}{729} a^{2} - \frac{114433}{729} a - \frac{1729327}{243} \) |
\( \bigl[a^{2} - 5\) , \( 0\) , \( a + 1\) , \( -a^{2} + 4\) , \( -a^{2} + a + 2\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+4\right){x}-a^{2}+a+2$ |
| 9.2-a1 |
9.2-a |
$4$ |
$4$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.33038$ |
$(a), (a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$54.81782187$ |
1.631453892 |
\( \frac{6119738}{729} a^{2} + \frac{6387025}{243} a + \frac{7273555}{729} \) |
\( \bigl[a^{2} - 5\) , \( -a + 1\) , \( a^{2} - a - 4\) , \( -5 a^{2} + 4 a + 12\) , \( -11 a^{2} + 29 a + 26\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a^{2}+4a+12\right){x}-11a^{2}+29a+26$ |
| 9.2-a2 |
9.2-a |
$4$ |
$4$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$4.33038$ |
$(a), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$27.40891093$ |
1.631453892 |
\( \frac{1562938292873}{531441} a^{2} - \frac{1250189673767}{177147} a - \frac{1945619955923}{531441} \) |
\( \bigl[a^{2} - 5\) , \( -a + 1\) , \( a^{2} - a - 4\) , \( -50 a^{2} + 109 a + 67\) , \( -459 a^{2} + 1093 a + 582\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-50a^{2}+109a+67\right){x}-459a^{2}+1093a+582$ |
| 9.2-a3 |
9.2-a |
$4$ |
$4$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{32} \) |
$4.33038$ |
$(a), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$13.70445546$ |
1.631453892 |
\( \frac{39726140295455}{282429536481} a^{2} - \frac{88745335080854}{94143178827} a + \frac{904943803858369}{282429536481} \) |
\( \bigl[a^{2} - 5\) , \( -a + 1\) , \( a^{2} - a - 4\) , \( -45 a^{2} + 134 a + 77\) , \( -427 a^{2} + 1003 a + 536\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-45a^{2}+134a+77\right){x}-427a^{2}+1003a+536$ |
| 9.2-a4 |
9.2-a |
$4$ |
$4$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.33038$ |
$(a), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$3.426113867$ |
1.631453892 |
\( \frac{64744115586859225}{729} a^{2} - \frac{51744856766349082}{243} a - \frac{81008808081585001}{729} \) |
\( \bigl[a^{2} - 5\) , \( -a + 1\) , \( a^{2} - a - 4\) , \( -775 a^{2} + 1764 a + 937\) , \( -26643 a^{2} + 63259 a + 33072\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-775a^{2}+1764a+937\right){x}-26643a^{2}+63259a+33072$ |
| 9.2-b1 |
9.2-b |
$4$ |
$4$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.33038$ |
$(a), (a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.336679175$ |
$237.5568231$ |
1.785245946 |
\( \frac{6119738}{729} a^{2} + \frac{6387025}{243} a + \frac{7273555}{729} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -15 a^{2} + 34 a + 24\) , \( 96 a^{2} - 230 a - 121\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-15a^{2}+34a+24\right){x}+96a^{2}-230a-121$ |
| 9.2-b2 |
9.2-b |
$4$ |
$4$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$4.33038$ |
$(a), (a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.673358350$ |
$118.7784115$ |
1.785245946 |
\( \frac{1562938292873}{531441} a^{2} - \frac{1250189673767}{177147} a - \frac{1945619955923}{531441} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -240 a^{2} + 574 a + 304\) , \( 4880 a^{2} - 11700 a - 6108\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-240a^{2}+574a+304\right){x}+4880a^{2}-11700a-6108$ |
| 9.2-b3 |
9.2-b |
$4$ |
$4$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( - 3^{32} \) |
$4.33038$ |
$(a), (a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.346716700$ |
$14.84730144$ |
1.785245946 |
\( \frac{39726140295455}{282429536481} a^{2} - \frac{88745335080854}{94143178827} a + \frac{904943803858369}{282429536481} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -250 a^{2} + 599 a + 314\) , \( 4473 a^{2} - 10722 a - 5605\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-250a^{2}+599a+314\right){x}+4473a^{2}-10722a-5605$ |
| 9.2-b4 |
9.2-b |
$4$ |
$4$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.33038$ |
$(a), (a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.336679175$ |
$59.38920577$ |
1.785245946 |
\( \frac{64744115586859225}{729} a^{2} - \frac{51744856766349082}{243} a - \frac{81008808081585001}{729} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a^{2} - a - 4\) , \( -3830 a^{2} + 9189 a + 4774\) , \( 297403 a^{2} - 713078 a - 372099\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-3830a^{2}+9189a+4774\right){x}+297403a^{2}-713078a-372099$ |
| 9.4-a1 |
9.4-a |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{7} \) |
$4.33038$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$124.2118108$ |
3.696714597 |
\( \frac{1182513561599}{3} a^{2} + 1118842847236 a + \frac{1249808156902}{3} \) |
\( \bigl[a\) , \( a^{2} - 6\) , \( 1\) , \( -92 a^{2} - 255 a - 84\) , \( 1250 a^{2} + 3547 a + 1315\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-92a^{2}-255a-84\right){x}+1250a^{2}+3547a+1315$ |
| 9.4-a2 |
9.4-a |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.33038$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$124.2118108$ |
3.696714597 |
\( \frac{1364027}{9} a^{2} + \frac{1290553}{3} a + \frac{1441468}{9} \) |
\( \bigl[a\) , \( a^{2} - 6\) , \( 1\) , \( -7 a^{2} - 15 a + 6\) , \( 15 a^{2} + 39 a + 7\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(-7a^{2}-15a+6\right){x}+15a^{2}+39a+7$ |
| 9.4-a3 |
9.4-a |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{9} \) |
$4.33038$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$124.2118108$ |
3.696714597 |
\( -\frac{10034922804609001}{27} a^{2} + \frac{1474490452082767}{9} a + \frac{68294559348248932}{27} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a\) , \( 244 a^{2} - 112 a - 1671\) , \( -3359 a^{2} + 1493 a + 22889\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(244a^{2}-112a-1671\right){x}-3359a^{2}+1493a+22889$ |
| 9.4-a4 |
9.4-a |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{12} \) |
$4.33038$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$124.2118108$ |
3.696714597 |
\( \frac{5548052552}{729} a^{2} - \frac{815029481}{243} a - \frac{37757035502}{729} \) |
\( \bigl[1\) , \( -a^{2} + 5\) , \( a\) , \( 14 a^{2} - 7 a - 96\) , \( -34 a^{2} + 15 a + 230\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(14a^{2}-7a-96\right){x}-34a^{2}+15a+230$ |
| 9.4-b1 |
9.4-b |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{7} \) |
$4.33038$ |
$(a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$108.9974712$ |
0.360434988 |
\( \frac{1182513561599}{3} a^{2} + 1118842847236 a + \frac{1249808156902}{3} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( 2 a^{2} - 29\) , \( 37 a^{2} - 21 a - 240\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(2a^{2}-29\right){x}+37a^{2}-21a-240$ |
| 9.4-b2 |
9.4-b |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{8} \) |
$4.33038$ |
$(a)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$108.9974712$ |
0.360434988 |
\( \frac{1364027}{9} a^{2} + \frac{1290553}{3} a + \frac{1441468}{9} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( -3 a^{2} + 16\) , \( -2 a^{2} + 12\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-3a^{2}+16\right){x}-2a^{2}+12$ |
| 9.4-b3 |
9.4-b |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{9} \) |
$4.33038$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$12.11083014$ |
0.360434988 |
\( -\frac{10034922804609001}{27} a^{2} + \frac{1474490452082767}{9} a + \frac{68294559348248932}{27} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 15029 a^{2} - 6624 a - 102288\) , \( 1796834 a^{2} - 792057 a - 12228698\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(15029a^{2}-6624a-102288\right){x}+1796834a^{2}-792057a-12228698$ |
| 9.4-b4 |
9.4-b |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{12} \) |
$4.33038$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$12.11083014$ |
0.360434988 |
\( \frac{5548052552}{729} a^{2} - \frac{815029481}{243} a - \frac{37757035502}{729} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 939 a^{2} - 414 a - 6393\) , \( 28087 a^{2} - 12381 a - 191153\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(939a^{2}-414a-6393\right){x}+28087a^{2}-12381a-191153$ |
| 17.1-a1 |
17.1-a |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$4.81460$ |
$(a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.249009758$ |
$169.8809087$ |
3.776897740 |
\( -\frac{635333}{17} a^{2} - \frac{1625995}{17} a - \frac{242032}{17} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + a + 4\) , \( a^{2} - 4\) , \( 4 a^{2} - 14 a + 2\) , \( -47 a^{2} + 109 a + 66\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(4a^{2}-14a+2\right){x}-47a^{2}+109a+66$ |
| 17.1-a2 |
17.1-a |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$4.81460$ |
$(a^2-a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.747029275$ |
$56.62696959$ |
3.776897740 |
\( -\frac{401083814}{4913} a^{2} + \frac{725586167}{4913} a + \frac{1173139856}{4913} \) |
\( \bigl[a\) , \( a - 1\) , \( a^{2} - a - 4\) , \( -11316 a^{2} + 27133 a + 14159\) , \( -1478065 a^{2} + 3543901 a + 1849381\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11316a^{2}+27133a+14159\right){x}-1478065a^{2}+3543901a+1849381$ |
| 17.1-b1 |
17.1-b |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$4.81460$ |
$(a^2-a-4)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.019076751$ |
$377.1202270$ |
1.926991409 |
\( -\frac{635333}{17} a^{2} - \frac{1625995}{17} a - \frac{242032}{17} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -7 a - 3\) , \( 8 a^{2} - a - 2\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a-3\right){x}+8a^{2}-a-2$ |
| 17.1-b2 |
17.1-b |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$4.81460$ |
$(a^2-a-4)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.019076751$ |
$125.7067423$ |
1.926991409 |
\( -\frac{401083814}{4913} a^{2} + \frac{725586167}{4913} a + \frac{1173139856}{4913} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( a^{2} - a - 5\) , \( -2234 a^{2} + 5354 a + 2802\) , \( 127672 a^{2} - 306112 a - 159752\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-2234a^{2}+5354a+2802\right){x}+127672a^{2}-306112a-159752$ |
| 19.1-a1 |
19.1-a |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$4.90469$ |
$(-a^2-a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$2.851714474$ |
$15.31159601$ |
3.898529149 |
\( -\frac{11923591168}{6859} a^{2} + \frac{28591403008}{6859} a + \frac{14920290304}{6859} \) |
\( \bigl[0\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 5\) , \( -10 a^{2} + 22 a + 19\) , \( -54 a^{2} + 145 a + 21\bigr] \) |
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(-10a^{2}+22a+19\right){x}-54a^{2}+145a+21$ |
| 19.1-a2 |
19.1-a |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$4.90469$ |
$(-a^2-a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.950571491$ |
$45.93478804$ |
3.898529149 |
\( \frac{11005952}{19} a^{2} - \frac{4861952}{19} a - \frac{74928128}{19} \) |
\( \bigl[0\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 4\) , \( 10 a^{2} - 7 a - 60\) , \( 19 a^{2} - 11 a - 126\bigr] \) |
${y}^2+\left(a^{2}-4\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(10a^{2}-7a-60\right){x}+19a^{2}-11a-126$ |
| 19.1-b1 |
19.1-b |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$4.90469$ |
$(-a^2-a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.035446905$ |
$391.8577597$ |
1.240169548 |
\( \frac{11005952}{19} a^{2} - \frac{4861952}{19} a - \frac{74928128}{19} \) |
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a^{2} - 5\) , \( -3 a^{2} - 10 a - 1\) , \( 11 a^{2} + 27 a + 4\bigr] \) |
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-3a^{2}-10a-1\right){x}+11a^{2}+27a+4$ |
| 19.1-b2 |
19.1-b |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$4.90469$ |
$(-a^2-a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.106340716$ |
$130.6192532$ |
1.240169548 |
\( -\frac{11923591168}{6859} a^{2} + \frac{28591403008}{6859} a + \frac{14920290304}{6859} \) |
\( \bigl[0\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -2 a^{2} + 4 a + 6\) , \( a^{2} - 3 a - 3\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-2a^{2}+4a+6\right){x}+a^{2}-3a-3$ |
| 24.2-a1 |
24.2-a |
$1$ |
$1$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{15} \cdot 3^{7} \) |
$5.09942$ |
$(a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$18.30973923$ |
3.814461432 |
\( -\frac{2562158506859}{69984} a^{2} - \frac{47868240929}{2187} a - \frac{58626468463}{23328} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + a + 5\) , \( a^{2} - 5\) , \( -173 a^{2} + 381 a + 224\) , \( 2741 a^{2} - 6693 a - 3451\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-173a^{2}+381a+224\right){x}+2741a^{2}-6693a-3451$ |
| 24.2-b1 |
24.2-b |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$5.09942$ |
$(a+1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$2.689638386$ |
0.720426090 |
\( -\frac{34470214007981}{24} a^{2} + \frac{15194741468753}{24} a + 9774730166859 \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 6\) , \( 1\) , \( -193 a^{2} - 525 a - 158\) , \( -4160 a^{2} - 11785 a - 4350\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-193a^{2}-525a-158\right){x}-4160a^{2}-11785a-4350$ |
| 24.2-b2 |
24.2-b |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{3} \cdot 3^{3} \) |
$5.09942$ |
$(a+1), (2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$72.62023642$ |
0.720426090 |
\( -\frac{179051}{54} a^{2} + \frac{44194}{27} a + \frac{415541}{18} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 6\) , \( 1\) , \( 2 a^{2} + 25 a + 47\) , \( -33 a^{2} - 74 a + 12\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(2a^{2}+25a+47\right){x}-33a^{2}-74a+12$ |
| 24.2-c1 |
24.2-c |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{9} \cdot 3 \) |
$5.09942$ |
$(a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.300433549$ |
$57.09639112$ |
1.531550675 |
\( -\frac{34470214007981}{24} a^{2} + \frac{15194741468753}{24} a + 9774730166859 \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 6\) , \( a + 1\) , \( 5 a - 24\) , \( -2 a^{2} - 21 a + 47\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(5a-24\right){x}-2a^{2}-21a+47$ |
| 24.2-c2 |
24.2-c |
$2$ |
$3$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{3} \cdot 3^{3} \) |
$5.09942$ |
$(a+1), (2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.100144516$ |
$171.2891733$ |
1.531550675 |
\( -\frac{179051}{54} a^{2} + \frac{44194}{27} a + \frac{415541}{18} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 6\) , \( a + 1\) , \( 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+{x}$ |
| 24.2-d1 |
24.2-d |
$1$ |
$1$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
24.2 |
\( 2^{3} \cdot 3 \) |
\( 2^{15} \cdot 3^{7} \) |
$5.09942$ |
$(a+1), (2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 1 \) |
$1$ |
$1.926934955$ |
1.481154978 |
\( -\frac{2562158506859}{69984} a^{2} - \frac{47868240929}{2187} a - \frac{58626468463}{23328} \) |
\( \bigl[1\) , \( a^{2} - a - 4\) , \( a^{2} - 5\) , \( -832 a^{2} + 1998 a + 1031\) , \( -30911 a^{2} + 74118 a + 38663\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-832a^{2}+1998a+1031\right){x}-30911a^{2}+74118a+38663$ |
| 27.1-a1 |
27.1-a |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{37} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$1.182996264$ |
2.253286300 |
\( \frac{398092198305618758756672}{1853020188851841} a^{2} + \frac{376665820516177558166902}{617673396283947} a + \frac{420765014530370948087545}{1853020188851841} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -241 a^{2} - 657 a - 254\) , \( -5653 a^{2} - 15839 a - 5884\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-241a^{2}-657a-254\right){x}-5653a^{2}-15839a-5884$ |
| 27.1-a2 |
27.1-a |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{14} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$37.85588046$ |
2.253286300 |
\( -\frac{113624322151340515972}{6561} a^{2} + \frac{50086477418823404924}{6561} a + \frac{257763916523688686789}{2187} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( 19 a^{2} + 13 a - 79\) , \( -55 a^{2} + 54 a + 440\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(19a^{2}+13a-79\right){x}-55a^{2}+54a+440$ |
| 27.1-a3 |
27.1-a |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{26} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$9.463970116$ |
2.253286300 |
\( \frac{2261405226768644}{43046721} a^{2} - \frac{1807175611576916}{14348907} a - \frac{2828449287531743}{43046721} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -21 a^{2} - 27 a - 9\) , \( -119 a^{2} - 128 a - 24\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-21a^{2}-27a-9\right){x}-119a^{2}-128a-24$ |
| 27.1-a4 |
27.1-a |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{16} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$75.71176092$ |
2.253286300 |
\( -\frac{340826049208}{6561} a^{2} + \frac{50070500680}{2187} a + \frac{2319647768305}{6561} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -a^{2} - 7 a - 4\) , \( a^{2} + 11 a + 14\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-a^{2}-7a-4\right){x}+a^{2}+11a+14$ |
| 27.1-a5 |
27.1-a |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{8} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$151.4235218$ |
2.253286300 |
\( \frac{8172560}{81} a^{2} + \frac{7490512}{27} a + \frac{6898081}{81} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -a^{2} - 7 a + 1\) , \( 5 a^{2} + 10 a + 2\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-a^{2}-7a+1\right){x}+5a^{2}+10a+2$ |
| 27.1-a6 |
27.1-a |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{25} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$64$ |
\( 2^{2} \) |
$1$ |
$1.182996264$ |
2.253286300 |
\( \frac{1217234252512590754932416}{43046721} a^{2} - \frac{2918515753506175444980194}{43046721} a - \frac{507675596306062380167843}{14348907} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( a + 1\) , \( -121 a^{2} + 283 a + 156\) , \( -2105 a^{2} + 3727 a + 2064\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-121a^{2}+283a+156\right){x}-2105a^{2}+3727a+2064$ |
| 27.1-b1 |
27.1-b |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{8} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$14.22855769$ |
1.905576647 |
\( -\frac{13554012859}{729} a^{2} - \frac{38418473716}{729} a - \frac{4731401608}{243} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 0\) , \( 61 a^{2} - 146 a - 77\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(61a^{2}-146a-77\right){x}$ |
| 27.1-b2 |
27.1-b |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{7} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2^{2} \) |
$1$ |
$7.114278846$ |
1.905576647 |
\( \frac{159871529818326538}{27} a^{2} + \frac{453790421722988191}{27} a + \frac{56323150121602070}{9} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( 0\) , \( -244 a^{2} + 584 a + 308\) , \( -825 a^{2} + 1982 a + 1021\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-244a^{2}+584a+308\right){x}-825a^{2}+1982a+1021$ |
| 27.1-b3 |
27.1-b |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{8} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$42.68567308$ |
1.905576647 |
\( -\frac{134339}{27} a^{2} + \frac{140557}{27} a + \frac{678424}{27} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 1723 a^{2} - 745 a - 11762\) , \( -66712 a^{2} + 29462 a + 453869\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(1723a^{2}-745a-11762\right){x}-66712a^{2}+29462a+453869$ |
| 27.1-b4 |
27.1-b |
$4$ |
$6$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{13} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$21.34283654$ |
1.905576647 |
\( \frac{19839404797}{729} a^{2} - \frac{47464260626}{729} a - \frac{24777620294}{729} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -1057 a^{2} + 690 a + 6563\) , \( -258397 a^{2} + 116954 a + 1749914\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1057a^{2}+690a+6563\right){x}-258397a^{2}+116954a+1749914$ |
| 27.1-c1 |
27.1-c |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{37} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$4.847513997$ |
1.154149553 |
\( \frac{398092198305618758756672}{1853020188851841} a^{2} + \frac{376665820516177558166902}{617673396283947} a + \frac{420765014530370948087545}{1853020188851841} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( -73022 a^{2} - 207268 a - 77184\) , \( -31534042 a^{2} - 89508412 a - 33328576\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-73022a^{2}-207268a-77184\right){x}-31534042a^{2}-89508412a-33328576$ |
| 27.1-c2 |
27.1-c |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{26} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$19.39005598$ |
1.154149553 |
\( \frac{2261405226768644}{43046721} a^{2} - \frac{1807175611576916}{14348907} a - \frac{2828449287531743}{43046721} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( -4582 a^{2} - 13003 a - 4849\) , \( -491566 a^{2} - 1395298 a - 519544\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-4582a^{2}-13003a-4849\right){x}-491566a^{2}-1395298a-519544$ |
| 27.1-c3 |
27.1-c |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{16} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$38.78011197$ |
1.154149553 |
\( -\frac{340826049208}{6561} a^{2} + \frac{50070500680}{2187} a + \frac{2319647768305}{6561} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( -572 a^{2} - 1628 a - 614\) , \( 9710 a^{2} + 27562 a + 10260\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-572a^{2}-1628a-614\right){x}+9710a^{2}+27562a+10260$ |
| 27.1-c4 |
27.1-c |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{8} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$77.56022395$ |
1.154149553 |
\( \frac{8172560}{81} a^{2} + \frac{7490512}{27} a + \frac{6898081}{81} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( -482 a^{2} - 1373 a - 519\) , \( 16530 a^{2} + 46920 a + 17468\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-482a^{2}-1373a-519\right){x}+16530a^{2}+46920a+17468$ |
| 27.1-c5 |
27.1-c |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( 3^{25} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$4.847513997$ |
1.154149553 |
\( \frac{1217234252512590754932416}{43046721} a^{2} - \frac{2918515753506175444980194}{43046721} a - \frac{507675596306062380167843}{14348907} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( -302 a^{2} - 738 a - 274\) , \( -1366834 a^{2} - 3880324 a - 1444888\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-302a^{2}-738a-274\right){x}-1366834a^{2}-3880324a-1444888$ |
| 27.1-c6 |
27.1-c |
$6$ |
$8$ |
3.3.1129.1 |
$3$ |
$[3, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{14} \) |
$5.20051$ |
$(a), (a+1), (a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$4.847513997$ |
1.154149553 |
\( -\frac{113624322151340515972}{6561} a^{2} + \frac{50086477418823404924}{6561} a + \frac{257763916523688686789}{2187} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( a^{2} - a - 4\) , \( 1998 a^{2} + 5667 a + 2101\) , \( 78186 a^{2} + 221930 a + 82632\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(1998a^{2}+5667a+2101\right){x}+78186a^{2}+221930a+82632$ |
*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.
