| 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 |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{4} \) |
$2.49952$ |
$(-a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.463177856$ |
$245.5100312$ |
0.760536356 |
\( \frac{5466989921733}{16} a^{2} - \frac{11727254606787}{16} a - \frac{7645773613401}{16} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - a - 4\) , \( a^{2} - a - 3\) , \( -2 a^{2} - 3 a - 5\) , \( 2 a^{2} + 5 a + 1\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-2a^{2}-3a-5\right){x}+2a^{2}+5a+1$ |
| 2.1-a2 |
2.1-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{6} \) |
$2.49952$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 2 \) |
$0.308785237$ |
$163.6733541$ |
0.760536356 |
\( -\frac{1571643}{64} a^{2} + \frac{787725}{64} a + \frac{9224631}{64} \) |
\( \bigl[a^{2} - 4\) , \( -1\) , \( a^{2} - a - 4\) , \( 5 a^{2} - 3 a - 30\) , \( 12 a^{2} - 6 a - 70\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-{x}^{2}+\left(5a^{2}-3a-30\right){x}+12a^{2}-6a-70$ |
| 2.1-a3 |
2.1-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$2.49952$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$0.154392618$ |
$163.6733541$ |
0.760536356 |
\( -\frac{1539}{8} a^{2} + \frac{2349}{8} a + \frac{16335}{8} \) |
\( \bigl[a^{2} - 4\) , \( -1\) , \( a^{2} - a - 4\) , \( 4870798 a^{2} + 13000543 a + 5474690\) , \( 7027580342 a^{2} + 18757167732 a + 7898882095\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}-{x}^{2}+\left(4870798a^{2}+13000543a+5474690\right){x}+7027580342a^{2}+18757167732a+7898882095$ |
| 2.1-a4 |
2.1-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$2.49952$ |
$(-a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$0.463177856$ |
$491.0200624$ |
0.760536356 |
\( -\frac{209947635}{2} a^{2} + \frac{109992987}{2} a + \frac{1202011713}{2} \) |
\( \bigl[a\) , \( a^{2} - a - 3\) , \( a + 1\) , \( -2807733302 a^{2} - 7494062245 a - 3155845004\) , \( 229857827468862 a^{2} + 613508720575135 a + 258356331752748\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-2807733302a^{2}-7494062245a-3155845004\right){x}+229857827468862a^{2}+613508720575135a+258356331752748$ |
| 2.1-a5 |
2.1-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$2.49952$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$0.617570475$ |
$40.91833853$ |
0.760536356 |
\( -\frac{26181894141}{8} a^{2} + \frac{13694926851}{8} a + \frac{149976258561}{8} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 2842829 a^{2} - 1489575 a - 16276475\) , \( 4197519584 a^{2} - 2199401188 a - 24032683196\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(2842829a^{2}-1489575a-16276475\right){x}+4197519584a^{2}-2199401188a-24032683196$ |
| 2.1-a6 |
2.1-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{2} \) |
$2.49952$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 2 \) |
$0.926355713$ |
$491.0200624$ |
0.760536356 |
\( \frac{349421337}{4} a^{2} + \frac{928661445}{4} a + \frac{390758859}{4} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - a - 3\) , \( -324 a^{2} - 871 a - 367\) , \( 8530 a^{2} + 22770 a + 9588\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-324a^{2}-871a-367\right){x}+8530a^{2}+22770a+9588$ |
| 2.1-a7 |
2.1-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{12} \) |
$2.49952$ |
$(-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.154392618$ |
$81.83667707$ |
0.760536356 |
\( \frac{28809189}{4096} a^{2} + \frac{39903597}{4096} a + \frac{12938967}{4096} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( 0\) , \( 30 a^{2} - 15 a - 170\) , \( 1575 a^{2} - 825 a - 9017\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(30a^{2}-15a-170\right){x}+1575a^{2}-825a-9017$ |
| 2.1-a8 |
2.1-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$2.49952$ |
$(-a-1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 1 \) |
$1.852711427$ |
$122.7550156$ |
0.760536356 |
\( \frac{233506890597662991}{2} a^{2} + \frac{623248358664043881}{2} a + \frac{262457817330484575}{2} \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 5\) , \( 1\) , \( 215 a^{2} - 108 a - 1240\) , \( 2267 a^{2} - 1197 a - 12954\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(215a^{2}-108a-1240\right){x}+2267a^{2}-1197a-12954$ |
| 3.1-a1 |
3.1-a |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{8} \) |
$2.67427$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$22.86965719$ |
1.835455460 |
\( -\frac{4864257163858}{9} a^{2} + \frac{7646267837608}{27} a + \frac{9283351677427}{3} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 3\) , \( a^{2} - 4\) , \( 2753065 a^{2} - 1442542 a - 15762534\) , \( 4005913593 a^{2} - 2099004172 a - 22935652916\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(2753065a^{2}-1442542a-15762534\right){x}+4005913593a^{2}-2099004172a-22935652916$ |
| 3.1-a2 |
3.1-a |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{4} \) |
$2.67427$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$182.9572575$ |
1.835455460 |
\( -\frac{2668076}{9} a^{2} + \frac{337588}{3} a + \frac{5441171}{3} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 3\) , \( a^{2} - 4\) , \( 172090 a^{2} - 90172 a - 985294\) , \( 62840112 a^{2} - 32926736 a - 359787841\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(172090a^{2}-90172a-985294\right){x}+62840112a^{2}-32926736a-359787841$ |
| 3.1-a3 |
3.1-a |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$2.67427$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$182.9572575$ |
1.835455460 |
\( \frac{445348577272}{3} a^{2} + 396223315968 a + 166854722323 \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - 4\) , \( 5246 a^{2} - 2751 a - 30034\) , \( -325215 a^{2} + 170404 a + 1862002\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5246a^{2}-2751a-30034\right){x}-325215a^{2}+170404a+1862002$ |
| 3.1-a4 |
3.1-a |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( 3^{2} \) |
$2.67427$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$365.9145150$ |
1.835455460 |
\( \frac{294352}{3} a^{2} + \frac{786496}{3} a + 112633 \) |
\( \bigl[a\) , \( -a + 1\) , \( a^{2} - 4\) , \( 656 a^{2} - 346 a - 3754\) , \( 7170 a^{2} - 3758 a - 41051\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(656a^{2}-346a-3754\right){x}+7170a^{2}-3758a-41051$ |
| 3.1-a5 |
3.1-a |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{2} \) |
$2.67427$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$91.47862876$ |
1.835455460 |
\( \frac{16546630718}{3} a^{2} - \frac{35494158640}{3} a - 7713667273 \) |
\( \bigl[1\) , \( a\) , \( a^{2} - a - 4\) , \( 2733518 a^{2} - 1432298 a - 15650617\) , \( 7412073534 a^{2} - 3883751585 a - 42437447041\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+a{x}^{2}+\left(2733518a^{2}-1432298a-15650617\right){x}+7412073534a^{2}-3883751585a-42437447041$ |
| 3.1-a6 |
3.1-a |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$2.67427$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$182.9572575$ |
1.835455460 |
\( -\frac{244}{3} a^{2} - 444 a + 1133 \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -7 a^{2} + 4 a + 42\) , \( 10 a^{2} - 5 a - 57\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-7a^{2}+4a+42\right){x}+10a^{2}-5a-57$ |
| 3.1-b1 |
3.1-b |
$2$ |
$5$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{5} \) |
$2.67427$ |
$(-a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$85.01274363$ |
0.682288777 |
\( \frac{335872}{9} a^{2} - \frac{262144}{9} a - 233472 \) |
\( \bigl[0\) , \( a^{2} - a - 5\) , \( 1\) , \( 6508997 a^{2} - 3410561 a - 37266928\) , \( -14611636367 a^{2} + 7656152579 a + 83658174958\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(6508997a^{2}-3410561a-37266928\right){x}-14611636367a^{2}+7656152579a+83658174958$ |
| 3.1-b2 |
3.1-b |
$2$ |
$5$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
3.1 |
\( 3 \) |
\( -3 \) |
$2.67427$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$0.680101949$ |
0.682288777 |
\( -\frac{40606410660136307924992}{3} a^{2} - 36127240514390937600000 a - 15213640854032899846144 \) |
\( \bigl[0\) , \( a^{2} - 5\) , \( 1\) , \( -326 a^{2} + 301 a + 1520\) , \( 3832 a^{2} - 769 a - 25247\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(-326a^{2}+301a+1520\right){x}+3832a^{2}-769a-25247$ |
| 6.1-a1 |
6.1-a |
$4$ |
$4$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{4} \cdot 3^{5} \) |
$3.00176$ |
$(-a-1), (-a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$181.3416296$ |
1.819247232 |
\( -\frac{107343409}{48} a^{2} + \frac{632115317}{144} a + \frac{946003829}{48} \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a\) , \( -3 a - 8\) , \( 2 a + 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-3a-8\right){x}+2a+3$ |
| 6.1-a2 |
6.1-a |
$4$ |
$4$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{5} \) |
$3.00176$ |
$(-a-1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$181.3416296$ |
1.819247232 |
\( \frac{192965}{6} a^{2} - \frac{1162105}{18} a - \frac{252931}{6} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 5\) , \( 0\) , \( -492762773 a^{2} - 1315222814 a - 553857065\) , \( -15501697485481 a^{2} - 41375256591378 a - 17423647227471\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(-492762773a^{2}-1315222814a-553857065\right){x}-15501697485481a^{2}-41375256591378a-17423647227471$ |
| 6.1-a3 |
6.1-a |
$4$ |
$4$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3^{10} \) |
$3.00176$ |
$(-a-1), (-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$181.3416296$ |
1.819247232 |
\( -\frac{134519}{324} a^{2} + \frac{90779}{108} a + \frac{21783}{4} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( a\) , \( -12 a^{2} - 30 a - 7\) , \( 46 a^{2} + 122 a + 49\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-12a^{2}-30a-7\right){x}+46a^{2}+122a+49$ |
| 6.1-a4 |
6.1-a |
$4$ |
$4$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{20} \) |
$3.00176$ |
$(-a-1), (-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$22.66770370$ |
1.819247232 |
\( \frac{178329943}{4374} a^{2} - \frac{401008297}{4374} a - \frac{65930071}{1458} \) |
\( \bigl[1\) , \( a^{2} - a - 5\) , \( a\) , \( 23 a^{2} + 65 a + 33\) , \( 268 a^{2} + 717 a + 300\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(23a^{2}+65a+33\right){x}+268a^{2}+717a+300$ |
| 8.1-a1 |
8.1-a |
$2$ |
$3$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{29} \) |
$3.14919$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$46.46722047$ |
1.864665325 |
\( -\frac{1631400670906281}{2048} a^{2} - \frac{4354337415066993}{2048} a - \frac{1833666912957879}{2048} \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 5\) , \( 1\) , \( -89 a^{2} + 171 a + 133\) , \( 2719 a^{2} - 5819 a - 3782\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-89a^{2}+171a+133\right){x}+2719a^{2}-5819a-3782$ |
| 8.1-a2 |
8.1-a |
$2$ |
$3$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{39} \) |
$3.14919$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$15.48907349$ |
1.864665325 |
\( -\frac{12247091572509}{8589934592} a^{2} - \frac{33703875052389}{8589934592} a - \frac{14465648733759}{8589934592} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( a + 1\) , \( 24 a^{2} - 15 a - 129\) , \( 872 a^{2} - 447 a - 5021\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(24a^{2}-15a-129\right){x}+872a^{2}-447a-5021$ |
| 8.1-b1 |
8.1-b |
$2$ |
$5$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{15} \) |
$3.14919$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 5 \) |
$1$ |
$144.2839272$ |
1.157982911 |
\( \frac{43747}{16} a^{2} - \frac{61963}{32} a - \frac{121975}{8} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 2 a - 5\) , \( a^{2} - 3\) , \( 4 a^{2} - 9 a - 11\) , \( 2 a^{2} - 5 a - 5\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(4a^{2}-9a-11\right){x}+2a^{2}-5a-5$ |
| 8.1-b2 |
8.1-b |
$2$ |
$5$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{51} \) |
$3.14919$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$1.154271418$ |
1.157982911 |
\( -\frac{38209767720213}{8388608} a^{2} + \frac{327852451117045}{33554432} a + \frac{213749253814679}{33554432} \) |
\( \bigl[a^{2} - 4\) , \( -a + 1\) , \( 0\) , \( -10274 a^{2} + 5388 a + 58811\) , \( 18029167 a^{2} - 9446842 a - 103225114\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10274a^{2}+5388a+58811\right){x}+18029167a^{2}-9446842a-103225114$ |
| 8.1-c1 |
8.1-c |
$4$ |
$6$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{18} \) |
$3.14919$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.057788465$ |
0.729272032 |
\( \frac{3384752311853731}{32} a^{2} + \frac{4517085807268307}{16} a + \frac{7608809330544671}{64} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 3\) , \( a^{2} - a - 3\) , \( 2936 a^{2} - 1535 a - 16807\) , \( 271509 a^{2} - 142261 a - 1554510\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(2936a^{2}-1535a-16807\right){x}+271509a^{2}-142261a-1554510$ |
| 8.1-c2 |
8.1-c |
$4$ |
$6$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$3.14919$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$163.5602885$ |
0.729272032 |
\( \frac{17651949}{2} a^{2} - 18895716 a - \frac{49294393}{4} \) |
\( \bigl[a^{2} - 4\) , \( a^{2} - 3\) , \( a^{2} - a - 3\) , \( -309 a^{2} + 165 a + 1773\) , \( -7644 a^{2} + 4008 a + 43768\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-309a^{2}+165a+1773\right){x}-7644a^{2}+4008a+43768$ |
| 8.1-c3 |
8.1-c |
$4$ |
$6$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{27} \) |
$3.14919$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.057788465$ |
0.729272032 |
\( -\frac{11916959145}{4096} a^{2} - \frac{28064196953}{4096} a - \frac{2679109859}{2048} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( 188 a^{2} - 99 a - 1071\) , \( 2416 a^{2} - 1265 a - 13835\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(188a^{2}-99a-1071\right){x}+2416a^{2}-1265a-13835$ |
| 8.1-c4 |
8.1-c |
$4$ |
$6$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$3.14919$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$163.5602885$ |
0.729272032 |
\( -\frac{30873}{16} a^{2} + \frac{41319}{16} a + \frac{54745}{8} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( 8 a^{2} - 4 a - 41\) , \( -8 a^{2} + 5 a + 46\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(8a^{2}-4a-41\right){x}-8a^{2}+5a+46$ |
| 9.1-a1 |
9.1-a |
$2$ |
$5$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{7} \) |
$3.21162$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$33.93037453$ |
2.723158056 |
\( -\frac{40606410660136307924992}{3} a^{2} - 36127240514390937600000 a - 15213640854032899846144 \) |
\( \bigl[0\) , \( a^{2} - a - 3\) , \( 1\) , \( -4004 a^{2} + 8541 a + 5577\) , \( 267480 a^{2} - 573570 a - 373975\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-4004a^{2}+8541a+5577\right){x}+267480a^{2}-573570a-373975$ |
| 9.1-a2 |
9.1-a |
$2$ |
$5$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{11} \) |
$3.21162$ |
$(-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$33.93037453$ |
2.723158056 |
\( \frac{335872}{9} a^{2} - \frac{262144}{9} a - 233472 \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 1\) , \( 4111 a^{2} - 2157 a - 23529\) , \( 233931 a^{2} - 122571 a - 1339369\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(4111a^{2}-2157a-23529\right){x}+233931a^{2}-122571a-1339369$ |
| 9.1-b1 |
9.1-b |
$4$ |
$27$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$3.21162$ |
$(-a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$2.392243879$ |
$1.837900525$ |
1.058602473 |
\( -12288000 \) |
\( \bigl[0\) , \( a^{2} - 3\) , \( 1\) , \( 9180 a^{2} - 4809 a - 52557\) , \( 761961 a^{2} - 399249 a - 4362568\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(9180a^{2}-4809a-52557\right){x}+761961a^{2}-399249a-4362568$ |
| 9.1-b2 |
9.1-b |
$4$ |
$27$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$3.21162$ |
$(-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$0.797414626$ |
$49.62331419$ |
1.058602473 |
\( 0 \) |
\( \bigl[0\) , \( a^{2} - 3\) , \( 1\) , \( a + 3\) , \( 3045 a^{2} - 1595 a - 17433\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(a+3\right){x}+3045a^{2}-1595a-17433$ |
| 9.1-b3 |
9.1-b |
$4$ |
$27$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$3.21162$ |
$(-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$0.265804875$ |
$148.8699425$ |
1.058602473 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^{3}$ |
| 9.1-b4 |
9.1-b |
$4$ |
$27$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$3.21162$ |
$(-a)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-27$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.088601625$ |
$446.6098277$ |
1.058602473 |
\( -12288000 \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 1\) , \( 78 a^{2} - 43 a - 441\) , \( -548 a^{2} + 288 a + 3135\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(78a^{2}-43a-441\right){x}-548a^{2}+288a+3135$ |
| 9.1-c1 |
9.1-c |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{7} \) |
$3.21162$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$54.59943124$ |
1.095499851 |
\( -\frac{244}{3} a^{2} - 444 a + 1133 \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - 3\) , \( -2 a^{2} - a + 12\) , \( -5 a^{2} - 4 a + 11\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-2a^{2}-a+12\right){x}-5a^{2}-4a+11$ |
| 9.1-c2 |
9.1-c |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$3.21162$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$54.59943124$ |
1.095499851 |
\( \frac{16546630718}{3} a^{2} - \frac{35494158640}{3} a - 7713667273 \) |
\( \bigl[a^{2} - 4\) , \( -a^{2} + 2 a + 5\) , \( a + 1\) , \( 1713 a^{2} - 881 a - 9847\) , \( -113493 a^{2} + 59505 a + 649702\bigr] \) |
${y}^2+\left(a^{2}-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(1713a^{2}-881a-9847\right){x}-113493a^{2}+59505a+649702$ |
| 9.1-c3 |
9.1-c |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$3.21162$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$27.29971562$ |
1.095499851 |
\( -\frac{4864257163858}{9} a^{2} + \frac{7646267837608}{27} a + \frac{9283351677427}{3} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 1738 a^{2} - 911 a - 9951\) , \( -63114 a^{2} + 33075 a + 361343\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(1738a^{2}-911a-9951\right){x}-63114a^{2}+33075a+361343$ |
| 9.1-c4 |
9.1-c |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$3.21162$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$109.1988624$ |
1.095499851 |
\( -\frac{2668076}{9} a^{2} + \frac{337588}{3} a + \frac{5441171}{3} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 108 a^{2} - 56 a - 621\) , \( -972 a^{2} + 513 a + 5555\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(108a^{2}-56a-621\right){x}-972a^{2}+513a+5555$ |
| 9.1-c5 |
9.1-c |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{7} \) |
$3.21162$ |
$(-a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$27.29971562$ |
1.095499851 |
\( \frac{445348577272}{3} a^{2} + 396223315968 a + 166854722323 \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 5\) , \( 0\) , \( -12\) , \( 12 a^{2} - 24 a - 63\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}-12{x}+12a^{2}-24a-63$ |
| 9.1-c6 |
9.1-c |
$6$ |
$8$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{8} \) |
$3.21162$ |
$(-a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$109.1988624$ |
1.095499851 |
\( \frac{294352}{3} a^{2} + \frac{786496}{3} a + 112633 \) |
\( \bigl[1\) , \( -a^{2} + 2 a + 5\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+3{x}$ |
| 12.2-a1 |
12.2-a |
$1$ |
$1$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$3.36936$ |
$(-a-1), (-a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$25.15679629$ |
1.009507461 |
\( -\frac{4096}{3} a^{2} + 4096 a \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 5\) , \( a^{2} - a - 4\) , \( 4\) , \( a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+4{x}+a-1$ |
| 16.2-a1 |
16.2-a |
$1$ |
$1$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{6} \) |
$3.53485$ |
$(-a-1), (a^2-a-5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$46.91567381$ |
1.882661138 |
\( -1689 a^{2} + \frac{821}{2} a + \frac{277}{2} \) |
\( \bigl[a^{2} - a - 4\) , \( -a^{2} + 4\) , \( 0\) , \( -12 a^{2} + 22 a + 28\) , \( -41 a^{2} + 85 a + 65\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-12a^{2}+22a+28\right){x}-41a^{2}+85a+65$ |
| 16.2-b1 |
16.2-b |
$2$ |
$3$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{10} \) |
$3.53485$ |
$(-a-1), (a^2-a-5)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$0.100989150$ |
$184.7894684$ |
2.246608453 |
\( -\frac{29789055}{8} a^{2} + \frac{63888759}{8} a + 5207940 \) |
\( \bigl[a^{2} - a - 4\) , \( -1\) , \( 0\) , \( -43 a^{2} + 92 a + 61\) , \( 289 a^{2} - 620 a - 404\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}={x}^{3}-{x}^{2}+\left(-43a^{2}+92a+61\right){x}+289a^{2}-620a-404$ |
| 16.2-b2 |
16.2-b |
$2$ |
$3$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.2 |
\( 2^{4} \) |
\( - 2^{6} \) |
$3.53485$ |
$(-a-1), (a^2-a-5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$0.302967450$ |
$61.59648949$ |
2.246608453 |
\( \frac{29565}{2} a^{2} - 7452 a - \frac{168021}{2} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( -a^{2} + 8 a + 1\) , \( 99 a^{2} - 206 a - 137\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+8a+1\right){x}+99a^{2}-206a-137$ |
| 16.3-a1 |
16.3-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{16} \) |
$3.53485$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$26.95710236$ |
1.081751255 |
\( \frac{5466989921733}{16} a^{2} - \frac{11727254606787}{16} a - \frac{7645773613401}{16} \) |
\( \bigl[a^{2} - a - 4\) , \( -a - 1\) , \( a^{2} - 3\) , \( -7138 a^{2} - 19054 a - 8027\) , \( 897541 a^{2} + 2395607 a + 1008819\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7138a^{2}-19054a-8027\right){x}+897541a^{2}+2395607a+1008819$ |
| 16.3-a2 |
16.3-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{18} \) |
$3.53485$ |
$(-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$107.8284094$ |
1.081751255 |
\( -\frac{1571643}{64} a^{2} + \frac{787725}{64} a + \frac{9224631}{64} \) |
\( \bigl[a^{2} - a - 4\) , \( a - 1\) , \( a + 1\) , \( -608 a^{2} - 1625 a - 686\) , \( 8551 a^{2} + 22822 a + 9608\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-608a^{2}-1625a-686\right){x}+8551a^{2}+22822a+9608$ |
| 16.3-a3 |
16.3-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{15} \) |
$3.53485$ |
$(-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$107.8284094$ |
1.081751255 |
\( -\frac{1539}{8} a^{2} + \frac{2349}{8} a + \frac{16335}{8} \) |
\( \bigl[a^{2} - a - 4\) , \( a - 1\) , \( a + 1\) , \( 19243798971 a^{2} + 51363221412 a + 21629706354\) , \( 1744617433374617 a^{2} + 4656521908472909 a + 1960920649785671\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(19243798971a^{2}+51363221412a+21629706354\right){x}+1744617433374617a^{2}+4656521908472909a+1960920649785671$ |
| 16.3-a4 |
16.3-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{24} \) |
$3.53485$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1$ |
$26.95710236$ |
1.081751255 |
\( \frac{28809189}{4096} a^{2} + \frac{39903597}{4096} a + \frac{12938967}{4096} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 3\) , \( a + 1\) , \( -27 a^{2} - 79 a - 44\) , \( -165 a^{2} - 647 a - 629\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-27a^{2}-79a-44\right){x}-165a^{2}-647a-629$ |
| 16.3-a5 |
16.3-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{13} \) |
$3.53485$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$53.91420473$ |
1.081751255 |
\( \frac{233506890597662991}{2} a^{2} + \frac{623248358664043881}{2} a + \frac{262457817330484575}{2} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + a + 3\) , \( 0\) , \( -3 a^{2} - 84 a - 164\) , \( 291 a^{2} + 437 a - 402\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-3a^{2}-84a-164\right){x}+291a^{2}+437a-402$ |
| 16.3-a6 |
16.3-a |
$8$ |
$12$ |
3.3.621.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( 2^{15} \) |
$3.53485$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$53.91420473$ |
1.081751255 |
\( -\frac{26181894141}{8} a^{2} + \frac{13694926851}{8} a + \frac{149976258561}{8} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 318018 a^{2} - 166637 a - 1820794\) , \( 156771774 a^{2} - 82144711 a - 897588754\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(318018a^{2}-166637a-1820794\right){x}+156771774a^{2}-82144711a-897588754$ |
*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.
