| 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 |
| 3.1-a1 |
3.1-a |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$4.28318$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$9.262087244$ |
$5.361523959$ |
1.866295847 |
\( \frac{3647418087153401600}{9} a^{2} + \frac{12152505188399579675}{9} a + \frac{7663079297127489302}{9} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + 5\) , \( 0\) , \( -8966 a^{2} - 29851 a - 18782\) , \( -1610710 a^{2} - 5366564 a - 3383997\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-8966a^{2}-29851a-18782\right){x}-1610710a^{2}-5366564a-3383997$ |
| 3.1-a2 |
3.1-a |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$4.28318$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.315521811$ |
$21.44609583$ |
1.866295847 |
\( \frac{83770515712}{729} a^{2} - \frac{211556539019}{729} a - \frac{225025497254}{729} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + 5\) , \( 0\) , \( -566 a^{2} - 1871 a - 1152\) , \( -25000 a^{2} - 83286 a - 52501\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-566a^{2}-1871a-1152\right){x}-25000a^{2}-83286a-52501$ |
| 3.1-a3 |
3.1-a |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$4.28318$ |
$(a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$4.631043622$ |
$42.89219167$ |
1.866295847 |
\( \frac{3486712051}{27} a^{2} + 430243828 a + \frac{7325174444}{27} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + 5\) , \( 0\) , \( -566 a^{2} - 1861 a - 1127\) , \( -25231 a^{2} - 84035 a - 52935\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-566a^{2}-1861a-1127\right){x}-25231a^{2}-84035a-52935$ |
| 3.1-a4 |
3.1-a |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$4.28318$ |
$(a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.315521811$ |
$85.78438335$ |
1.866295847 |
\( -\frac{18455}{9} a^{2} - \frac{74249}{9} a - \frac{45272}{9} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + 5\) , \( 0\) , \( -41 a^{2} - 111 a - 22\) , \( -409 a^{2} - 1330 a - 778\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{2}+5\right){x}^{2}+\left(-41a^{2}-111a-22\right){x}-409a^{2}-1330a-778$ |
| 3.1-b1 |
3.1-b |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$4.28318$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$116.2040551$ |
1.455738608 |
\( \frac{28888}{3} a^{2} - 8465 a - \frac{236119}{3} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a^{2} - 5\) , \( -3 a^{2} + 6 a + 14\) , \( 2 a - 6\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-3a^{2}+6a+14\right){x}+2a-6$ |
| 3.1-b2 |
3.1-b |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$4.28318$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$58.10202757$ |
1.455738608 |
\( -\frac{5616238583}{9} a^{2} + \frac{4744413139}{9} a + \frac{46539348691}{9} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a^{2} - 5\) , \( -23 a^{2} + 56 a + 69\) , \( -151 a^{2} + 377 a + 420\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-23a^{2}+56a+69\right){x}-151a^{2}+377a+420$ |
| 3.1-c1 |
3.1-c |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$4.28318$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$218.5874629$ |
2.738339972 |
\( \frac{28888}{3} a^{2} - 8465 a - \frac{236119}{3} \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( a + 1\) , \( -7 a^{2} + 14 a + 24\) , \( 6 a^{2} - 17 a - 15\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-7a^{2}+14a+24\right){x}+6a^{2}-17a-15$ |
| 3.1-c2 |
3.1-c |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$4.28318$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$109.2937314$ |
2.738339972 |
\( -\frac{5616238583}{9} a^{2} + \frac{4744413139}{9} a + \frac{46539348691}{9} \) |
\( \bigl[a\) , \( -a^{2} + a + 6\) , \( a + 1\) , \( -52 a^{2} + 124 a + 149\) , \( -402 a^{2} + 995 a + 1131\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-52a^{2}+124a+149\right){x}-402a^{2}+995a+1131$ |
| 3.1-d1 |
3.1-d |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{4} \) |
$4.28318$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.930693752$ |
$56.05573469$ |
1.960695801 |
\( \frac{3647418087153401600}{9} a^{2} + \frac{12152505188399579675}{9} a + \frac{7663079297127489302}{9} \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{2} + 6\) , \( 1\) , \( -448 a^{2} - 1615 a - 1246\) , \( 20408 a^{2} + 68330 a + 43708\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-448a^{2}-1615a-1246\right){x}+20408a^{2}+68330a+43708$ |
| 3.1-d2 |
3.1-d |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{16} \) |
$4.28318$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$3.722775011$ |
$14.01393367$ |
1.960695801 |
\( \frac{83770515712}{729} a^{2} - \frac{211556539019}{729} a - \frac{225025497254}{729} \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{2} + 6\) , \( 1\) , \( 72 a^{2} - 185 a - 906\) , \( 1828 a^{2} - 84 a - 11516\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(72a^{2}-185a-906\right){x}+1828a^{2}-84a-11516$ |
| 3.1-d3 |
3.1-d |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$4.28318$ |
$(a+2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.861387505$ |
$112.1114693$ |
1.960695801 |
\( \frac{3486712051}{27} a^{2} + 430243828 a + \frac{7325174444}{27} \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{2} + 6\) , \( 1\) , \( -28 a^{2} - 100 a - 76\) , \( 386 a^{2} + 1145 a + 460\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-28a^{2}-100a-76\right){x}+386a^{2}+1145a+460$ |
| 3.1-d4 |
3.1-d |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$4.28318$ |
$(a+2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.930693752$ |
$224.2229387$ |
1.960695801 |
\( -\frac{18455}{9} a^{2} - \frac{74249}{9} a - \frac{45272}{9} \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{2} + 6\) , \( 1\) , \( -8 a^{2} + 49\) , \( 31 a + 77\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-8a^{2}+49\right){x}+31a+77$ |
| 7.3-a1 |
7.3-a |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{4} \) |
$4.93283$ |
$(a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$6.758261312$ |
2.709237478 |
\( \frac{891057753305283132}{2401} a^{2} + \frac{2968835409481386780}{2401} a + \frac{267439520969258193}{343} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 6\) , \( 37 a^{2} - 64 a - 373\) , \( -245 a^{2} + 49 a + 1648\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(37a^{2}-64a-373\right){x}-245a^{2}+49a+1648$ |
| 7.3-a2 |
7.3-a |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{2} \) |
$4.93283$ |
$(a-3)$ |
$0 \le r \le 2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$16$ |
\( 2 \) |
$1$ |
$13.51652262$ |
2.709237478 |
\( \frac{1916321832}{49} a^{2} - \frac{5880191400}{49} a - \frac{904973625}{7} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 6\) , \( -8 a^{2} + a + 67\) , \( -7 a^{2} + 54\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-8a^{2}+a+67\right){x}-7a^{2}+54$ |
| 7.3-b1 |
7.3-b |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( -7 \) |
$4.93283$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$370.4075559$ |
2.320128067 |
\( -\frac{18778104}{7} a^{2} - \frac{45129447}{7} a + 563571 \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -11 a^{2} + 27 a + 31\) , \( -37 a^{2} + 92 a + 104\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-11a^{2}+27a+31\right){x}-37a^{2}+92a+104$ |
| 7.3-b2 |
7.3-b |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{2} \) |
$4.93283$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$185.2037779$ |
2.320128067 |
\( \frac{5182034348525841}{49} a^{2} + \frac{17265555469905147}{49} a + \frac{1555320941467317}{7} \) |
\( \bigl[a\) , \( -1\) , \( 1\) , \( -56 a^{2} + 137 a + 156\) , \( 454 a^{2} - 1128 a - 1277\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-56a^{2}+137a+156\right){x}+454a^{2}-1128a-1277$ |
| 7.3-c1 |
7.3-c |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{12} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$2.024164009$ |
$33.65829893$ |
2.560479086 |
\( -\frac{60482347370793}{13841287201} a^{2} + \frac{53847599505804}{13841287201} a + \frac{73714568155812}{1977326743} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 7\) , \( a^{2} - 6\) , \( 366 a^{2} - 909 a - 1039\) , \( 12295 a^{2} - 30578 a - 34612\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(366a^{2}-909a-1039\right){x}+12295a^{2}-30578a-34612$ |
| 7.3-c2 |
7.3-c |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{6} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.012082004$ |
$67.31659786$ |
2.560479086 |
\( \frac{62897553}{117649} a^{2} - \frac{108050193}{117649} a - \frac{19374120}{16807} \) |
\( \bigl[a^{2} - a - 5\) , \( a^{2} - a - 7\) , \( a^{2} - 6\) , \( -159 a^{2} + 396 a + 441\) , \( 1625 a^{2} - 4041 a - 4581\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-159a^{2}+396a+441\right){x}+1625a^{2}-4041a-4581$ |
| 7.3-c3 |
7.3-c |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{4} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$6.072492027$ |
$11.21943297$ |
2.560479086 |
\( -\frac{9569439498469401}{2401} a^{2} + \frac{8083960822225413}{2401} a + \frac{11328033562517304}{343} \) |
\( \bigl[1\) , \( -a^{2} + 6\) , \( a^{2} - 6\) , \( -130 a^{2} - 428 a - 265\) , \( -2573 a^{2} - 8592 a - 5450\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-130a^{2}-428a-265\right){x}-2573a^{2}-8592a-5450$ |
| 7.3-c4 |
7.3-c |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{2} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$3.036246013$ |
$22.43886595$ |
2.560479086 |
\( \frac{247023681714}{49} a^{2} - \frac{614299252419}{49} a - \frac{99353154330}{7} \) |
\( \bigl[1\) , \( -a^{2} + 6\) , \( a^{2} - 6\) , \( -10 a^{2} - 23 a\) , \( -32 a^{2} - 110 a - 72\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-10a^{2}-23a\right){x}-32a^{2}-110a-72$ |
| 7.3-d1 |
7.3-d |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{3} \) |
$4.93283$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$120.2744265$ |
2.260094875 |
\( -\frac{33777}{343} a^{2} - \frac{78084}{343} a + \frac{87588}{49} \) |
\( \bigl[a^{2} - a - 6\) , \( 0\) , \( a^{2} - a - 6\) , \( -1445 a^{2} + 3594 a + 4065\) , \( -7231 a^{2} + 17984 a + 20351\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-1445a^{2}+3594a+4065\right){x}-7231a^{2}+17984a+20351$ |
| 7.3-d2 |
7.3-d |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{6} \) |
$4.93283$ |
$(a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$60.13721329$ |
2.260094875 |
\( -\frac{11025580032}{117649} a^{2} + \frac{9913015629}{117649} a + \frac{16776984654}{16807} \) |
\( \bigl[a^{2} - a - 6\) , \( 0\) , \( a^{2} - a - 6\) , \( -15065 a^{2} + 37469 a + 42395\) , \( 2182222 a^{2} - 5427293 a - 6142049\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-15065a^{2}+37469a+42395\right){x}+2182222a^{2}-5427293a-6142049$ |
| 7.3-d3 |
7.3-d |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( -7 \) |
$4.93283$ |
$(a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$360.8232797$ |
2.260094875 |
\( \frac{35134146}{7} a^{2} - \frac{143996481}{7} a + 12820950 \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 5\) , \( a + 1\) , \( 16 a + 13\) , \( 10 a^{2} + 7 a - 1\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(16a+13\right){x}+10a^{2}+7a-1$ |
| 7.3-d4 |
7.3-d |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{2} \) |
$4.93283$ |
$(a-3)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$9$ |
\( 2 \) |
$1$ |
$180.4116398$ |
2.260094875 |
\( \frac{46302027726806595}{49} a^{2} - \frac{115155491504289867}{49} a - \frac{18617243030268894}{7} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 5\) , \( a + 1\) , \( -45 a^{2} + 126 a + 138\) , \( 371 a^{2} - 899 a - 1024\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-45a^{2}+126a+138\right){x}+371a^{2}-899a-1024$ |
| 7.3-e1 |
7.3-e |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{3} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.578186536$ |
$257.6699724$ |
2.799530229 |
\( -\frac{33777}{343} a^{2} - \frac{78084}{343} a + \frac{87588}{49} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( a^{2} - a - 6\) , \( -654 a^{2} + 1626 a + 1843\) , \( -1970 a^{2} + 4906 a + 5525\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-654a^{2}+1626a+1843\right){x}-1970a^{2}+4906a+5525$ |
| 7.3-e2 |
7.3-e |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{6} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.289093268$ |
$257.6699724$ |
2.799530229 |
\( -\frac{11025580032}{117649} a^{2} + \frac{9913015629}{117649} a + \frac{16776984654}{16807} \) |
\( \bigl[a^{2} - 5\) , \( -a^{2} + 6\) , \( a^{2} - a - 6\) , \( -6779 a^{2} + 16916 a + 18893\) , \( 665860 a^{2} - 1656212 a - 1873499\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-6779a^{2}+16916a+18893\right){x}+665860a^{2}-1656212a-1873499$ |
| 7.3-e3 |
7.3-e |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( -7 \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1.734559610$ |
$85.88999080$ |
2.799530229 |
\( \frac{35134146}{7} a^{2} - \frac{143996481}{7} a + 12820950 \) |
\( \bigl[a\) , \( -a\) , \( a^{2} - a - 6\) , \( 5 a^{2} - 4 a - 45\) , \( 15 a^{2} - 13 a - 124\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-a{x}^{2}+\left(5a^{2}-4a-45\right){x}+15a^{2}-13a-124$ |
| 7.3-e4 |
7.3-e |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{2} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.867279805$ |
$85.88999080$ |
2.799530229 |
\( \frac{46302027726806595}{49} a^{2} - \frac{115155491504289867}{49} a - \frac{18617243030268894}{7} \) |
\( \bigl[a\) , \( -a\) , \( a^{2} - a - 6\) , \( -15 a^{2} + 46 a + 10\) , \( 104 a^{2} - 236 a - 369\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-a{x}^{2}+\left(-15a^{2}+46a+10\right){x}+104a^{2}-236a-369$ |
| 7.3-f1 |
7.3-f |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{4} \) |
$4.93283$ |
$(a-3)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.723981403$ |
$168.3181247$ |
3.053165926 |
\( -\frac{9569439498469401}{2401} a^{2} + \frac{8083960822225413}{2401} a + \frac{11328033562517304}{343} \) |
\( \bigl[a^{2} - 6\) , \( -1\) , \( a^{2} - a - 6\) , \( 48 a^{2} - 68 a - 468\) , \( -279 a^{2} + 327 a + 2539\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-{x}^{2}+\left(48a^{2}-68a-468\right){x}-279a^{2}+327a+2539$ |
| 7.3-f2 |
7.3-f |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{2} \) |
$4.93283$ |
$(a-3)$ |
$2$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.723981403$ |
$336.6362495$ |
3.053165926 |
\( \frac{247023681714}{49} a^{2} - \frac{614299252419}{49} a - \frac{99353154330}{7} \) |
\( \bigl[a^{2} - 6\) , \( -1\) , \( a^{2} - a - 6\) , \( 3 a^{2} - 3 a - 28\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-{x}^{2}+\left(3a^{2}-3a-28\right){x}$ |
| 7.3-f3 |
7.3-f |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{12} \) |
$4.93283$ |
$(a-3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.080442378$ |
$56.10604158$ |
3.053165926 |
\( -\frac{60482347370793}{13841287201} a^{2} + \frac{53847599505804}{13841287201} a + \frac{73714568155812}{1977326743} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 6\) , \( 182 a^{2} - 426 a - 603\) , \( 3760 a^{2} - 9500 a - 10094\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(182a^{2}-426a-603\right){x}+3760a^{2}-9500a-10094$ |
| 7.3-f4 |
7.3-f |
$4$ |
$6$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{6} \) |
$4.93283$ |
$(a-3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \cdot 3 \) |
$0.080442378$ |
$112.2120831$ |
3.053165926 |
\( \frac{62897553}{117649} a^{2} - \frac{108050193}{117649} a - \frac{19374120}{16807} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - 6\) , \( -73 a^{2} + 179 a + 212\) , \( 443 a^{2} - 1107 a - 1236\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-73a^{2}+179a+212\right){x}+443a^{2}-1107a-1236$ |
| 7.3-g1 |
7.3-g |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( -7 \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$4.260078202$ |
$27.06818798$ |
2.166856399 |
\( -\frac{18778104}{7} a^{2} - \frac{45129447}{7} a + 563571 \) |
\( \bigl[a + 1\) , \( -a^{2} + 6\) , \( a^{2} - 5\) , \( -5 a^{2} + 10 a + 9\) , \( -6 a^{2} + 22 a - 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-5a^{2}+10a+9\right){x}-6a^{2}+22a-16$ |
| 7.3-g2 |
7.3-g |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{2} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.130039101$ |
$27.06818798$ |
2.166856399 |
\( \frac{5182034348525841}{49} a^{2} + \frac{17265555469905147}{49} a + \frac{1555320941467317}{7} \) |
\( \bigl[a + 1\) , \( -a^{2} + 6\) , \( a^{2} - 5\) , \( -25 a^{2} + 60 a + 64\) , \( 143 a^{2} - 349 a - 434\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-25a^{2}+60a+64\right){x}+143a^{2}-349a-434$ |
| 7.3-h1 |
7.3-h |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( - 7^{4} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.195935172$ |
$33.41463553$ |
1.501854078 |
\( \frac{891057753305283132}{2401} a^{2} + \frac{2968835409481386780}{2401} a + \frac{267439520969258193}{343} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 6\) , \( a^{2} - a - 5\) , \( -126 a^{2} - 433 a - 290\) , \( 2459 a^{2} + 8186 a + 5151\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-126a^{2}-433a-290\right){x}+2459a^{2}+8186a+5151$ |
| 7.3-h2 |
7.3-h |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
7.3 |
\( 7 \) |
\( 7^{2} \) |
$4.93283$ |
$(a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.597967586$ |
$66.82927107$ |
1.501854078 |
\( \frac{1916321832}{49} a^{2} - \frac{5880191400}{49} a - \frac{904973625}{7} \) |
\( \bigl[a^{2} - 5\) , \( a^{2} - 2 a - 6\) , \( a^{2} - a - 5\) , \( -6 a^{2} - 28 a - 25\) , \( 24 a^{2} + 77 a + 45\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-6a^{2}-28a-25\right){x}+24a^{2}+77a+45$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$5.04384$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$124.9261130$ |
3.130007221 |
\( -228 a^{2} + 191 a + \frac{3787}{2} \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( 0\) , \( 6 a^{2} - 15 a - 15\) , \( -133 a^{2} + 331 a + 374\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(6a^{2}-15a-15\right){x}-133a^{2}+331a+374$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{3} \) |
$5.04384$ |
$(2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$75.66027290$ |
1.895658120 |
\( -228 a^{2} + 191 a + \frac{3787}{2} \) |
\( \bigl[a + 1\) , \( a^{2} - 7\) , \( a^{2} - a - 5\) , \( a^{2} - a + 12\) , \( -42 a^{2} + 113 a + 113\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-7\right){x}^{2}+\left(a^{2}-a+12\right){x}-42a^{2}+113a+113$ |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{10} \) |
$5.14383$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$53.67198923$ |
2.689489168 |
\( \frac{3647418087153401600}{9} a^{2} + \frac{12152505188399579675}{9} a + \frac{7663079297127489302}{9} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - 6\) , \( -96 a^{2} - 336 a - 239\) , \( 1713 a^{2} + 5711 a + 3609\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(-96a^{2}-336a-239\right){x}+1713a^{2}+5711a+3609$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{22} \) |
$5.14383$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$26.83599461$ |
2.689489168 |
\( \frac{83770515712}{729} a^{2} - \frac{211556539019}{729} a - \frac{225025497254}{729} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - 6\) , \( 4 a^{2} - 26 a - 109\) , \( 93 a^{2} - 13 a - 549\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(4a^{2}-26a-109\right){x}+93a^{2}-13a-549$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$5.14383$ |
$(a+2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$107.3439784$ |
2.689489168 |
\( \frac{3486712051}{27} a^{2} + 430243828 a + \frac{7325174444}{27} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - 6\) , \( -6 a^{2} - 21 a - 14\) , \( 21 a^{2} + 59 a + 18\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(-6a^{2}-21a-14\right){x}+21a^{2}+59a+18$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$5.14383$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$107.3439784$ |
2.689489168 |
\( -\frac{18455}{9} a^{2} - \frac{74249}{9} a - \frac{45272}{9} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 7\) , \( a^{2} - 6\) , \( -a^{2} - a + 6\) , \( -a - 3\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(-a^{2}-a+6\right){x}-a-3$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$5.14383$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$116.1026409$ |
2.908936297 |
\( -\frac{5616238583}{9} a^{2} + \frac{4744413139}{9} a + \frac{46539348691}{9} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + 2 a + 7\) , \( 0\) , \( 134 a^{2} - 125 a - 1134\) , \( -1197 a^{2} + 913 a + 9672\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(134a^{2}-125a-1134\right){x}-1197a^{2}+913a+9672$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$5.14383$ |
$(a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$116.1026409$ |
2.908936297 |
\( \frac{28888}{3} a^{2} - 8465 a - \frac{236119}{3} \) |
\( \bigl[a^{2} - 6\) , \( -a^{2} + 2 a + 7\) , \( 0\) , \( 4 a^{2} - 19\) , \( -a^{2} + 3 a + 11\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}={x}^{3}+\left(-a^{2}+2a+7\right){x}^{2}+\left(4a^{2}-19\right){x}-a^{2}+3a+11$ |
| 9.1-c1 |
9.1-c |
$4$ |
$27$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$5.14383$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.422537555$ |
$49.62331419$ |
3.152059767 |
\( -12288000 \) |
\( \bigl[0\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 6\) , \( 31 a^{2} - 53 a - 311\) , \( -218 a^{2} + 300 a + 2103\bigr] \) |
${y}^2+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(31a^{2}-53a-311\right){x}-218a^{2}+300a+2103$ |
| 9.1-c2 |
9.1-c |
$4$ |
$27$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$5.14383$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.140845851$ |
$148.8699425$ |
3.152059767 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 6\) , \( a^{2} - 3 a - 1\) , \( a^{2} - 3 a - 5\bigr] \) |
${y}^2+\left(a^{2}-6\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(a^{2}-3a-1\right){x}+a^{2}-3a-5$ |
| 9.1-c3 |
9.1-c |
$4$ |
$27$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$5.14383$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.267612665$ |
$16.54110473$ |
3.152059767 |
\( -12288000 \) |
\( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 77 a^{2} - 24 a - 773\) , \( 1154 a^{2} - 1271 a - 8580\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(77a^{2}-24a-773\right){x}+1154a^{2}-1271a-8580$ |
| 9.1-c4 |
9.1-c |
$4$ |
$27$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$5.14383$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$3$ |
3Cs |
$1$ |
\( 2 \) |
$0.422537555$ |
$49.62331419$ |
3.152059767 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( a^{2} - 5\) , \( 0\) , \( 10 a^{2} - 10 a - 87\bigr] \) |
${y}^2+\left(a^{2}-5\right){y}={x}^{3}+10a^{2}-10a-87$ |
| 9.1-d1 |
9.1-d |
$4$ |
$27$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$5.14383$ |
$(a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$3.503917762$ |
$49.62331419$ |
2.904293640 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - 2 a - 5\) , \( a\) , \( a^{2} - 3 a - 1\) , \( -3963 a^{2} + 9856 a + 11152\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(a^{2}-3a-1\right){x}-3963a^{2}+9856a+11152$ |
| 9.1-d2 |
9.1-d |
$4$ |
$27$ |
3.3.1593.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$5.14383$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$10.51175328$ |
$1.837900525$ |
2.904293640 |
\( -12288000 \) |
\( \bigl[0\) , \( a^{2} - 2 a - 5\) , \( a\) , \( -8909 a^{2} + 22177 a + 25009\) , \( -1021158 a^{2} + 2539726 a + 2873946\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-8909a^{2}+22177a+25009\right){x}-1021158a^{2}+2539726a+2873946$ |
*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.
