| 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 |
| 1.1-a1 |
1.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$426.8772676$ |
1.222146061 |
\( 232596390030307355741184 a^{3} - 546232618788155566809606 a^{2} - 1356819799627224186865146 a + 2759940373949650789780995 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 4\) , \( -140 a^{3} - 160 a^{2} + 400 a + 486\) , \( 2472 a^{3} + 4986 a^{2} - 7874 a - 13623\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-4\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}^{2}+\left(-140a^{3}-160a^{2}+400a+486\right){x}+2472a^{3}+4986a^{2}-7874a-13623$ |
| 1.1-a2 |
1.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$426.8772676$ |
1.222146061 |
\( -915155982 a^{3} - 654076296 a^{2} + 7114850460 a + 8539320375 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( -\frac{3}{2} a^{3} + \frac{1}{2} a^{2} + \frac{19}{2} a + 7\) , \( -\frac{1}{2} a^{3} - \frac{3}{2} a^{2} + \frac{11}{2} a + 9\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}^{2}+\left(-\frac{3}{2}a^{3}+\frac{1}{2}a^{2}+\frac{19}{2}a+7\right){x}-\frac{1}{2}a^{3}-\frac{3}{2}a^{2}+\frac{11}{2}a+9$ |
| 1.1-a3 |
1.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$426.8772676$ |
1.222146061 |
\( -672696414 a^{3} + 2241928692 a^{2} + 824411520 a - 4613931855 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} + \frac{5}{4} a - 6\) , \( a^{2} - 4\) , \( \frac{1}{4} a^{3} - \frac{5}{4} a^{2} - \frac{5}{4} a + 6\) , \( -a^{2} + 4\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}+\frac{5}{4}a-6\right){x}^{2}+\left(\frac{1}{4}a^{3}-\frac{5}{4}a^{2}-\frac{5}{4}a+6\right){x}-a^{2}+4$ |
| 1.1-a4 |
1.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$1707.509070$ |
1.222146061 |
\( 194488565724 a^{3} - 194488565724 a^{2} - 972442828620 a + 1258756440921 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 4\) , \( -\frac{455}{4} a^{3} - \frac{1005}{4} a^{2} + \frac{1495}{4} a + 681\) , \( \frac{9923}{4} a^{3} + \frac{19793}{4} a^{2} - \frac{31511}{4} a - 13538\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-4\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}^{2}+\left(-\frac{455}{4}a^{3}-\frac{1005}{4}a^{2}+\frac{1495}{4}a+681\right){x}+\frac{9923}{4}a^{3}+\frac{19793}{4}a^{2}-\frac{31511}{4}a-13538$ |
| 1.1-a5 |
1.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$426.8772676$ |
1.222146061 |
\( 105727870471923450934272 a^{3} + 207908358285924760134150 a^{2} - 334801502883929846512134 a - 570259763104518729062451 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} + \frac{5}{4} a - 6\) , \( a + 1\) , \( -\frac{579}{2} a^{3} + \frac{1175}{2} a^{2} + \frac{3499}{2} a - 2803\) , \( \frac{24649}{4} a^{3} - \frac{59117}{4} a^{2} - \frac{143017}{4} a + 75255\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}+\frac{5}{4}a-6\right){x}^{2}+\left(-\frac{579}{2}a^{3}+\frac{1175}{2}a^{2}+\frac{3499}{2}a-2803\right){x}+\frac{24649}{4}a^{3}-\frac{59117}{4}a^{2}-\frac{143017}{4}a+75255$ |
| 1.1-a6 |
1.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$1707.509070$ |
1.222146061 |
\( 134136 a^{3} - 134136 a^{2} - 670680 a + 988065 \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{9}{4} a + 1\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -51 a^{3} - 100 a^{2} + 161 a + 277\) , \( \frac{2859}{4} a^{3} + \frac{5593}{4} a^{2} - \frac{9051}{4} a - 3840\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{9}{4}a+1\right){x}^{2}+\left(-51a^{3}-100a^{2}+161a+277\right){x}+\frac{2859}{4}a^{3}+\frac{5593}{4}a^{2}-\frac{9051}{4}a-3840$ |
| 1.1-b1 |
1.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3Nn |
$4$ |
\( 1 \) |
$1$ |
$73.41463559$ |
0.210185490 |
\( 194488565724 a^{3} - 194488565724 a^{2} - 972442828620 a + 1258756440921 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( a^{2} - 4\) , \( \frac{57}{2} a^{3} + \frac{55}{2} a^{2} - \frac{453}{2} a - 313\) , \( \frac{583}{4} a^{3} + \frac{461}{4} a^{2} - \frac{4563}{4} a - 1440\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}^{2}+\left(\frac{57}{2}a^{3}+\frac{55}{2}a^{2}-\frac{453}{2}a-313\right){x}+\frac{583}{4}a^{3}+\frac{461}{4}a^{2}-\frac{4563}{4}a-1440$ |
| 1.1-b2 |
1.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Nn |
$16$ |
\( 1 \) |
$1$ |
$4.588414724$ |
0.210185490 |
\( 105727870471923450934272 a^{3} + 207908358285924760134150 a^{2} - 334801502883929846512134 a - 570259763104518729062451 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( a^{2} - 4\) , \( -\frac{501}{4} a^{3} - \frac{335}{4} a^{2} + \frac{3869}{4} a + 1122\) , \( \frac{1061}{4} a^{3} + \frac{795}{4} a^{2} - \frac{8313}{4} a - 2563\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+\left(a^{2}-4\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}^{2}+\left(-\frac{501}{4}a^{3}-\frac{335}{4}a^{2}+\frac{3869}{4}a+1122\right){x}+\frac{1061}{4}a^{3}+\frac{795}{4}a^{2}-\frac{8313}{4}a-2563$ |
| 1.1-b3 |
1.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$1174.634169$ |
0.210185490 |
\( -672696414 a^{3} + 2241928692 a^{2} + 824411520 a - 4613931855 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( a + 1\) , \( -\frac{11}{2} a^{3} - \frac{15}{2} a^{2} + \frac{49}{2} a + 33\) , \( -12 a^{3} - 23 a^{2} + 42 a + 69\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}^{2}+\left(-\frac{11}{2}a^{3}-\frac{15}{2}a^{2}+\frac{49}{2}a+33\right){x}-12a^{3}-23a^{2}+42a+69$ |
| 1.1-b4 |
1.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$1174.634169$ |
0.210185490 |
\( -915155982 a^{3} - 654076296 a^{2} + 7114850460 a + 8539320375 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} + \frac{5}{4} a - 6\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( -\frac{15}{2} a^{3} + \frac{37}{2} a^{2} + \frac{85}{2} a - 94\) , \( -\frac{3}{4} a^{3} + \frac{7}{4} a^{2} + \frac{15}{4} a - 10\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}+\frac{5}{4}a-6\right){x}^{2}+\left(-\frac{15}{2}a^{3}+\frac{37}{2}a^{2}+\frac{85}{2}a-94\right){x}-\frac{3}{4}a^{3}+\frac{7}{4}a^{2}+\frac{15}{4}a-10$ |
| 1.1-b5 |
1.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2B, 3Nn |
$16$ |
\( 1 \) |
$1$ |
$4.588414724$ |
0.210185490 |
\( 232596390030307355741184 a^{3} - 546232618788155566809606 a^{2} - 1356819799627224186865146 a + 2759940373949650789780995 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} + \frac{5}{4} a - 6\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a + 1\) , \( -\frac{183}{2} a^{3} + \frac{597}{2} a^{2} + \frac{237}{2} a - 617\) , \( \frac{1401}{4} a^{3} - \frac{4729}{4} a^{2} - \frac{1697}{4} a + 2432\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}+\frac{5}{4}a-6\right){x}^{2}+\left(-\frac{183}{2}a^{3}+\frac{597}{2}a^{2}+\frac{237}{2}a-617\right){x}+\frac{1401}{4}a^{3}-\frac{4729}{4}a^{2}-\frac{1697}{4}a+2432$ |
| 1.1-b6 |
1.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.80294$ |
$\textsf{none}$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 1 \) |
$1$ |
$1174.634169$ |
0.210185490 |
\( 134136 a^{3} - 134136 a^{2} - 670680 a + 988065 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 5\) , \( a^{2} - a - 5\) , \( \frac{1}{2} a^{3} - \frac{15}{2} a^{2} + \frac{13}{2} a + 24\) , \( -\frac{15}{2} a^{3} + \frac{39}{2} a^{2} + \frac{25}{2} a - 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{15}{2}a^{2}+\frac{13}{2}a+24\right){x}-\frac{15}{2}a^{3}+\frac{39}{2}a^{2}+\frac{25}{2}a-38$ |
| 5.1-a1 |
5.1-a |
$4$ |
$4$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$9.54179$ |
$(-1/4a^3+1/4a^2+9/4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$371.9611438$ |
1.064921656 |
\( \frac{101721274789}{5} a^{3} + 40005919611 a^{2} - \frac{322114074601}{5} a - \frac{548649562547}{5} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -a^{2} + 2 a + 6\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( -\frac{11}{2} a^{3} - \frac{15}{2} a^{2} + \frac{51}{2} a + 35\) , \( -\frac{85}{4} a^{3} - \frac{155}{4} a^{2} + \frac{309}{4} a + 121\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-\frac{11}{2}a^{3}-\frac{15}{2}a^{2}+\frac{51}{2}a+35\right){x}-\frac{85}{4}a^{3}-\frac{155}{4}a^{2}+\frac{309}{4}a+121$ |
| 5.1-a2 |
5.1-a |
$4$ |
$4$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{6} \) |
$9.54179$ |
$(-1/4a^3+1/4a^2+9/4a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$743.9222876$ |
1.064921656 |
\( \frac{2054926}{25} a^{3} - \frac{2054926}{25} a^{2} - \frac{2054926}{5} a + \frac{14015337}{25} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -8 a^{3} + 29 a^{2} + 41 a - 162\) , \( 67 a^{3} - 142 a^{2} - 400 a + 689\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){x}^{2}+\left(-8a^{3}+29a^{2}+41a-162\right){x}+67a^{3}-142a^{2}-400a+689$ |
| 5.1-a3 |
5.1-a |
$4$ |
$4$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$9.54179$ |
$(-1/4a^3+1/4a^2+9/4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$371.9611438$ |
1.064921656 |
\( \frac{223782067836}{5} a^{3} - 105106588136 a^{2} - \frac{1305402638524}{5} a + \frac{2655351465237}{5} \) |
\( \bigl[1\) , \( a - 1\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( -\frac{1}{4} a^{3} + \frac{1}{4} a^{2} + \frac{5}{4} a + 1\) , \( \frac{3}{4} a^{3} + \frac{1}{4} a^{2} - \frac{23}{4} a - 6\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{1}{4}a^{3}+\frac{1}{4}a^{2}+\frac{5}{4}a+1\right){x}+\frac{3}{4}a^{3}+\frac{1}{4}a^{2}-\frac{23}{4}a-6$ |
| 5.1-a4 |
5.1-a |
$4$ |
$4$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{12} \) |
$9.54179$ |
$(-1/4a^3+1/4a^2+9/4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$185.9805719$ |
1.064921656 |
\( -\frac{10856747421}{125} a^{3} + \frac{10856747421}{125} a^{2} + \frac{10856747421}{25} a + \frac{26839589707}{125} \) |
\( \bigl[1\) , \( -a^{2} + a + 6\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a + 1\) , \( -\frac{185}{2} a^{3} + \frac{473}{2} a^{2} + \frac{1053}{2} a - 1231\) , \( \frac{633}{2} a^{3} - \frac{1251}{2} a^{2} - \frac{3843}{2} a + 2937\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a+1\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-\frac{185}{2}a^{3}+\frac{473}{2}a^{2}+\frac{1053}{2}a-1231\right){x}+\frac{633}{2}a^{3}-\frac{1251}{2}a^{2}-\frac{3843}{2}a+2937$ |
| 5.1-b1 |
5.1-b |
$4$ |
$4$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$9.54179$ |
$(-1/4a^3+1/4a^2+9/4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$371.9611438$ |
1.064921656 |
\( \frac{223782067836}{5} a^{3} - 105106588136 a^{2} - \frac{1305402638524}{5} a + \frac{2655351465237}{5} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{13}{4} a + 6\) , \( a\) , \( -13 a^{3} + 14 a^{2} + 87 a - 41\) , \( -\frac{169}{4} a^{3} + \frac{289}{4} a^{2} + \frac{1049}{4} a - 312\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+a{y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{3}{4}a^{2}+\frac{13}{4}a+6\right){x}^{2}+\left(-13a^{3}+14a^{2}+87a-41\right){x}-\frac{169}{4}a^{3}+\frac{289}{4}a^{2}+\frac{1049}{4}a-312$ |
| 5.1-b2 |
5.1-b |
$4$ |
$4$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{12} \) |
$9.54179$ |
$(-1/4a^3+1/4a^2+9/4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$185.9805719$ |
1.064921656 |
\( -\frac{10856747421}{125} a^{3} + \frac{10856747421}{125} a^{2} + \frac{10856747421}{25} a + \frac{26839589707}{125} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( a^{2} - 5\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 4\) , \( \frac{53}{2} a^{3} + \frac{37}{2} a^{2} - \frac{431}{2} a - 266\) , \( -\frac{829}{4} a^{3} - \frac{607}{4} a^{2} + \frac{6413}{4} a + 1935\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(\frac{53}{2}a^{3}+\frac{37}{2}a^{2}-\frac{431}{2}a-266\right){x}-\frac{829}{4}a^{3}-\frac{607}{4}a^{2}+\frac{6413}{4}a+1935$ |
| 5.1-b3 |
5.1-b |
$4$ |
$4$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{6} \) |
$9.54179$ |
$(-1/4a^3+1/4a^2+9/4a-2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3Ns |
$1$ |
\( 2 \) |
$1$ |
$743.9222876$ |
1.064921656 |
\( \frac{2054926}{25} a^{3} - \frac{2054926}{25} a^{2} - \frac{2054926}{5} a + \frac{14015337}{25} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( -1\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{25}{2} a^{3} + \frac{19}{2} a^{2} - \frac{197}{2} a - 122\) , \( -\frac{215}{4} a^{3} - \frac{153}{4} a^{2} + \frac{1671}{4} a + 500\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){y}={x}^{3}-{x}^{2}+\left(\frac{25}{2}a^{3}+\frac{19}{2}a^{2}-\frac{197}{2}a-122\right){x}-\frac{215}{4}a^{3}-\frac{153}{4}a^{2}+\frac{1671}{4}a+500$ |
| 5.1-b4 |
5.1-b |
$4$ |
$4$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
5.1 |
\( 5 \) |
\( 5^{3} \) |
$9.54179$ |
$(-1/4a^3+1/4a^2+9/4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3Ns |
$1$ |
\( 1 \) |
$1$ |
$371.9611438$ |
1.064921656 |
\( \frac{101721274789}{5} a^{3} + 40005919611 a^{2} - \frac{322114074601}{5} a - \frac{548649562547}{5} \) |
\( \bigl[1\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{9}{4} a\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( -\frac{1}{4} a^{3} + \frac{1}{4} a^{2} + \frac{5}{4} a + 1\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{1}{2} a + 2\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{9}{4}a\right){x}^{2}+\left(-\frac{1}{4}a^{3}+\frac{1}{4}a^{2}+\frac{5}{4}a+1\right){x}+\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{1}{2}a+2$ |
| 11.1-a1 |
11.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$108.5277066$ |
1.242855680 |
\( \frac{7273468393095067}{22} a^{3} + \frac{14302897799889049}{22} a^{2} - \frac{2093855705464743}{2} a - \frac{19615292432376359}{11} \) |
\( \bigl[a^{2} - 5\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{9}{4} a + 6\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( -\frac{39}{4} a^{3} + \frac{119}{4} a^{2} + \frac{43}{4} a - 44\) , \( \frac{267}{4} a^{3} - \frac{883}{4} a^{2} - \frac{415}{4} a + 498\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{3}{4}a^{2}+\frac{9}{4}a+6\right){x}^{2}+\left(-\frac{39}{4}a^{3}+\frac{119}{4}a^{2}+\frac{43}{4}a-44\right){x}+\frac{267}{4}a^{3}-\frac{883}{4}a^{2}-\frac{415}{4}a+498$ |
| 11.1-a2 |
11.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$868.2216528$ |
1.242855680 |
\( \frac{411160610}{121} a^{3} + \frac{808501635}{121} a^{2} - \frac{118325940}{11} a - \frac{2216159307}{121} \) |
\( \bigl[a^{2} - 5\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{9}{4} a + 6\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{11}{4} a^{3} - \frac{51}{4} a^{2} + \frac{13}{4} a + 31\) , \( \frac{17}{2} a^{3} - \frac{61}{2} a^{2} - \frac{13}{2} a + 66\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{3}{4}a^{2}+\frac{9}{4}a+6\right){x}^{2}+\left(\frac{11}{4}a^{3}-\frac{51}{4}a^{2}+\frac{13}{4}a+31\right){x}+\frac{17}{2}a^{3}-\frac{61}{2}a^{2}-\frac{13}{2}a+66$ |
| 11.1-a3 |
11.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$434.1108264$ |
1.242855680 |
\( \frac{68677413}{22} a^{3} - \frac{154526569}{22} a^{2} - \frac{39309977}{2} a + \frac{424778391}{11} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -2 a^{3} - a^{2} + 15 a + 17\) , \( -\frac{9}{4} a^{3} - \frac{7}{4} a^{2} + \frac{69}{4} a + 21\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}={x}^{3}+\left(-a^{2}+2a+4\right){x}^{2}+\left(-2a^{3}-a^{2}+15a+17\right){x}-\frac{9}{4}a^{3}-\frac{7}{4}a^{2}+\frac{69}{4}a+21$ |
| 11.1-a4 |
11.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$868.2216528$ |
1.242855680 |
\( -\frac{3103873072}{121} a^{3} + \frac{10344549461}{121} a^{2} + \frac{345806468}{11} a - \frac{21289260279}{121} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{9}{4} a\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( -\frac{17}{2} a^{3} - \frac{41}{2} a^{2} + \frac{55}{2} a + 55\) , \( \frac{225}{4} a^{3} + \frac{455}{4} a^{2} - \frac{725}{4} a - 313\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{9}{4}a\right){x}^{2}+\left(-\frac{17}{2}a^{3}-\frac{41}{2}a^{2}+\frac{55}{2}a+55\right){x}+\frac{225}{4}a^{3}+\frac{455}{4}a^{2}-\frac{725}{4}a-313$ |
| 11.1-a5 |
11.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$868.2216528$ |
1.242855680 |
\( -\frac{5464135}{14641} a^{3} + \frac{40719115}{14641} a^{2} - \frac{2073860}{1331} a + \frac{7578393}{14641} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a + 1\) , \( -a^{2} + 6\) , \( 0\) , \( \frac{1}{4} a^{3} - \frac{5}{4} a^{2} - \frac{5}{4} a + 7\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a+1\right){x}{y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(\frac{1}{4}a^{3}-\frac{5}{4}a^{2}-\frac{5}{4}a+7\right){x}$ |
| 11.1-a6 |
11.1-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$54.26385330$ |
1.242855680 |
\( \frac{854023677963652}{214358881} a^{3} - \frac{2476679916467461}{214358881} a^{2} - \frac{425755034425588}{19487171} a + \frac{13393536931873651}{214358881} \) |
\( \bigl[1\) , \( \frac{1}{4} a^{3} - \frac{5}{4} a^{2} - \frac{1}{4} a + 6\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( \frac{21}{4} a^{3} + \frac{19}{4} a^{2} - \frac{169}{4} a - 53\) , \( 27 a^{3} + 21 a^{2} - 211 a - 264\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{5}{4}a^{2}-\frac{1}{4}a+6\right){x}^{2}+\left(\frac{21}{4}a^{3}+\frac{19}{4}a^{2}-\frac{169}{4}a-53\right){x}+27a^{3}+21a^{2}-211a-264$ |
| 11.1-b1 |
11.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$365.7195229$ |
2.094103896 |
\( -\frac{3103873072}{121} a^{3} + \frac{10344549461}{121} a^{2} + \frac{345806468}{11} a - \frac{21289260279}{121} \) |
\( \bigl[a^{2} - 5\) , \( \frac{1}{4} a^{3} - \frac{5}{4} a^{2} + \frac{3}{4} a + 5\) , \( a^{2} - a - 5\) , \( \frac{5}{2} a^{3} - \frac{15}{2} a^{2} - \frac{5}{2} a + 18\) , \( \frac{13}{4} a^{3} - \frac{41}{4} a^{2} - \frac{17}{4} a + 22\bigr] \) |
${y}^2+\left(a^{2}-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{5}{4}a^{2}+\frac{3}{4}a+5\right){x}^{2}+\left(\frac{5}{2}a^{3}-\frac{15}{2}a^{2}-\frac{5}{2}a+18\right){x}+\frac{13}{4}a^{3}-\frac{41}{4}a^{2}-\frac{17}{4}a+22$ |
| 11.1-b2 |
11.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{8} \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$365.7195229$ |
2.094103896 |
\( \frac{854023677963652}{214358881} a^{3} - \frac{2476679916467461}{214358881} a^{2} - \frac{425755034425588}{19487171} a + \frac{13393536931873651}{214358881} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a + 1\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 4\) , \( 26 a^{3} + 21 a^{2} - 193 a - 234\) , \( -121 a^{3} - 57 a^{2} + 1049 a + 1221\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-4\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a+1\right){x}^{2}+\left(26a^{3}+21a^{2}-193a-234\right){x}-121a^{3}-57a^{2}+1049a+1221$ |
| 11.1-b3 |
11.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1462.878091$ |
2.094103896 |
\( \frac{411160610}{121} a^{3} + \frac{808501635}{121} a^{2} - \frac{118325940}{11} a - \frac{2216159307}{121} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} - \frac{3}{4} a - 6\) , \( a + 1\) , \( -\frac{3}{2} a^{3} - \frac{9}{2} a^{2} + \frac{15}{2} a + 16\) , \( \frac{25}{4} a^{3} + \frac{39}{4} a^{2} - \frac{81}{4} a - 30\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}-\frac{3}{4}a-6\right){x}^{2}+\left(-\frac{3}{2}a^{3}-\frac{9}{2}a^{2}+\frac{15}{2}a+16\right){x}+\frac{25}{4}a^{3}+\frac{39}{4}a^{2}-\frac{81}{4}a-30$ |
| 11.1-b4 |
11.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$182.8597614$ |
2.094103896 |
\( \frac{7273468393095067}{22} a^{3} + \frac{14302897799889049}{22} a^{2} - \frac{2093855705464743}{2} a - \frac{19615292432376359}{11} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} - \frac{3}{4} a - 6\) , \( a + 1\) , \( -\frac{111}{4} a^{3} - \frac{153}{4} a^{2} + \frac{335}{4} a + 116\) , \( \frac{1063}{4} a^{3} + \frac{2365}{4} a^{2} - \frac{3471}{4} a - 1594\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}-\frac{3}{4}a-6\right){x}^{2}+\left(-\frac{111}{4}a^{3}-\frac{153}{4}a^{2}+\frac{335}{4}a+116\right){x}+\frac{1063}{4}a^{3}+\frac{2365}{4}a^{2}-\frac{3471}{4}a-1594$ |
| 11.1-b5 |
11.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11^{4} \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1462.878091$ |
2.094103896 |
\( -\frac{5464135}{14641} a^{3} + \frac{40719115}{14641} a^{2} - \frac{2073860}{1331} a + \frac{7578393}{14641} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{9}{4} a + 5\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( -\frac{83}{4} a^{3} + \frac{183}{4} a^{2} + \frac{487}{4} a - 229\) , \( \frac{403}{4} a^{3} - \frac{951}{4} a^{2} - \frac{2351}{4} a + 1201\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{3}{4}a^{2}+\frac{9}{4}a+5\right){x}^{2}+\left(-\frac{83}{4}a^{3}+\frac{183}{4}a^{2}+\frac{487}{4}a-229\right){x}+\frac{403}{4}a^{3}-\frac{951}{4}a^{2}-\frac{2351}{4}a+1201$ |
| 11.1-b6 |
11.1-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.1 |
\( 11 \) |
\( 11 \) |
$10.53010$ |
$(1/4a^3-1/4a^2-9/4a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$731.4390458$ |
2.094103896 |
\( \frac{68677413}{22} a^{3} - \frac{154526569}{22} a^{2} - \frac{39309977}{2} a + \frac{424778391}{11} \) |
\( \bigl[1\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 4\) , \( a + 1\) , \( -\frac{3}{4} a^{3} + \frac{7}{4} a^{2} + \frac{43}{4} a - 19\) , \( -\frac{23}{4} a^{3} + \frac{67}{4} a^{2} + \frac{91}{4} a - 62\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-4\right){x}^{2}+\left(-\frac{3}{4}a^{3}+\frac{7}{4}a^{2}+\frac{43}{4}a-19\right){x}-\frac{23}{4}a^{3}+\frac{67}{4}a^{2}+\frac{91}{4}a-62$ |
| 11.2-a1 |
11.2-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$434.1108264$ |
1.242855680 |
\( \frac{49918907}{44} a^{3} + \frac{11070855}{4} a^{2} - \frac{71549171}{44} a - \frac{48978730}{11} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{13}{4} a + 4\) , \( a^{2} - a - 5\) , \( -\frac{13}{4} a^{3} - \frac{3}{4} a^{2} + \frac{93}{4} a + 22\) , \( -\frac{13}{4} a^{3} - \frac{11}{4} a^{2} + \frac{105}{4} a + 31\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{3}{4}a^{2}+\frac{13}{4}a+4\right){x}^{2}+\left(-\frac{13}{4}a^{3}-\frac{3}{4}a^{2}+\frac{93}{4}a+22\right){x}-\frac{13}{4}a^{3}-\frac{11}{4}a^{2}+\frac{105}{4}a+31$ |
| 11.2-a2 |
11.2-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$868.2216528$ |
1.242855680 |
\( \frac{3618522395}{484} a^{3} - \frac{772470125}{44} a^{2} - \frac{21109482815}{484} a + \frac{10734680853}{121} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( a^{2} - 2 a - 6\) , \( a + 1\) , \( \frac{15}{4} a^{3} + \frac{13}{4} a^{2} - \frac{135}{4} a - 43\) , \( \frac{29}{4} a^{3} + \frac{23}{4} a^{2} - \frac{229}{4} a - 70\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(\frac{15}{4}a^{3}+\frac{13}{4}a^{2}-\frac{135}{4}a-43\right){x}+\frac{29}{4}a^{3}+\frac{23}{4}a^{2}-\frac{229}{4}a-70$ |
| 11.2-a3 |
11.2-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$108.5277066$ |
1.242855680 |
\( \frac{32002584485363773}{44} a^{3} - \frac{6832301533757455}{4} a^{2} - \frac{186682780837545189}{44} a + \frac{94934003135225802}{11} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( a^{2} - 2 a - 6\) , \( a + 1\) , \( -15 a^{3} - 8 a^{2} + 115 a + 127\) , \( \frac{399}{4} a^{3} + \frac{301}{4} a^{2} - \frac{3075}{4} a - 934\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-15a^{3}-8a^{2}+115a+127\right){x}+\frac{399}{4}a^{3}+\frac{301}{4}a^{2}-\frac{3075}{4}a-934$ |
| 11.2-a4 |
11.2-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$868.2216528$ |
1.242855680 |
\( -\frac{16890310111}{484} a^{3} - \frac{1097490495}{44} a^{2} + \frac{131313527403}{484} a + \frac{39402009399}{121} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( a - 1\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( -\frac{77}{4} a^{3} + \frac{197}{4} a^{2} + \frac{437}{4} a - 254\) , \( 124 a^{3} - 293 a^{2} - 722 a + 1483\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-\frac{77}{4}a^{3}+\frac{197}{4}a^{2}+\frac{437}{4}a-254\right){x}+124a^{3}-293a^{2}-722a+1483$ |
| 11.2-a5 |
11.2-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$868.2216528$ |
1.242855680 |
\( -\frac{36734695}{58564} a^{3} - \frac{9480475}{5324} a^{2} + \frac{384206015}{58564} a + \frac{309995058}{14641} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a + 1\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} + \frac{5}{4} a - 4\) , \( 0\) , \( a^{2} - 3\) , \( 0\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a+1\right){x}{y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}+\frac{5}{4}a-4\right){x}^{2}+\left(a^{2}-3\right){x}$ |
| 11.2-a6 |
11.2-a |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{8} \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$54.26385330$ |
1.242855680 |
\( \frac{1380251484487591}{857435524} a^{3} + \frac{464579406320695}{77948684} a^{2} - \frac{5248509466985123}{857435524} a - \frac{3246212442027647}{214358881} \) |
\( \bigl[1\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 6\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a + 1\) , \( \frac{13}{4} a^{3} - \frac{61}{4} a^{2} + \frac{7}{4} a + 39\) , \( \frac{65}{4} a^{3} - \frac{213}{4} a^{2} - \frac{89}{4} a + 105\bigr] \) |
${y}^2+{x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-6\right){x}^{2}+\left(\frac{13}{4}a^{3}-\frac{61}{4}a^{2}+\frac{7}{4}a+39\right){x}+\frac{65}{4}a^{3}-\frac{213}{4}a^{2}-\frac{89}{4}a+105$ |
| 11.2-b1 |
11.2-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{8} \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$365.7195229$ |
2.094103896 |
\( \frac{1380251484487591}{857435524} a^{3} + \frac{464579406320695}{77948684} a^{2} - \frac{5248509466985123}{857435524} a - \frac{3246212442027647}{214358881} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( -\frac{1}{4} a^{3} + \frac{5}{4} a^{2} - \frac{3}{4} a - 6\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( \frac{45}{2} a^{3} - \frac{135}{2} a^{2} - \frac{107}{2} a + 167\) , \( -\frac{203}{4} a^{3} + \frac{855}{4} a^{2} - \frac{581}{4} a - 128\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{5}{4}a^{2}-\frac{3}{4}a-6\right){x}^{2}+\left(\frac{45}{2}a^{3}-\frac{135}{2}a^{2}-\frac{107}{2}a+167\right){x}-\frac{203}{4}a^{3}+\frac{855}{4}a^{2}-\frac{581}{4}a-128$ |
| 11.2-b2 |
11.2-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$365.7195229$ |
2.094103896 |
\( -\frac{16890310111}{484} a^{3} - \frac{1097490495}{44} a^{2} + \frac{131313527403}{484} a + \frac{39402009399}{121} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 5\) , \( a^{2} - 6\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( \frac{9}{2} a^{3} + \frac{7}{2} a^{2} - \frac{65}{2} a - 40\) , \( \frac{27}{2} a^{3} + \frac{19}{2} a^{2} - \frac{203}{2} a - 121\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-5\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){y}={x}^{3}+\left(a^{2}-6\right){x}^{2}+\left(\frac{9}{2}a^{3}+\frac{7}{2}a^{2}-\frac{65}{2}a-40\right){x}+\frac{27}{2}a^{3}+\frac{19}{2}a^{2}-\frac{203}{2}a-121$ |
| 11.2-b3 |
11.2-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$182.8597614$ |
2.094103896 |
\( \frac{32002584485363773}{44} a^{3} - \frac{6832301533757455}{4} a^{2} - \frac{186682780837545189}{44} a + \frac{94934003135225802}{11} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( \frac{1}{4} a^{3} - \frac{5}{4} a^{2} + \frac{3}{4} a + 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a + 1\) , \( -58 a^{3} + 125 a^{2} + 344 a - 605\) , \( \frac{2045}{4} a^{3} - \frac{4993}{4} a^{2} - \frac{11805}{4} a + 6389\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{5}{4}a^{2}+\frac{3}{4}a+5\right){x}^{2}+\left(-58a^{3}+125a^{2}+344a-605\right){x}+\frac{2045}{4}a^{3}-\frac{4993}{4}a^{2}-\frac{11805}{4}a+6389$ |
| 11.2-b4 |
11.2-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{2} \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1462.878091$ |
2.094103896 |
\( \frac{3618522395}{484} a^{3} - \frac{772470125}{44} a^{2} - \frac{21109482815}{484} a + \frac{10734680853}{121} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{5}{4} a\) , \( \frac{1}{4} a^{3} - \frac{5}{4} a^{2} + \frac{3}{4} a + 5\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a + 1\) , \( -3 a^{3} + 10 a^{2} + 14 a - 50\) , \( \frac{31}{4} a^{3} - \frac{75}{4} a^{2} - \frac{175}{4} a + 88\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{5}{4}a\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a+1\right){y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{5}{4}a^{2}+\frac{3}{4}a+5\right){x}^{2}+\left(-3a^{3}+10a^{2}+14a-50\right){x}+\frac{31}{4}a^{3}-\frac{75}{4}a^{2}-\frac{175}{4}a+88$ |
| 11.2-b5 |
11.2-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11 \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$731.4390458$ |
2.094103896 |
\( \frac{49918907}{44} a^{3} + \frac{11070855}{4} a^{2} - \frac{71549171}{44} a - \frac{48978730}{11} \) |
\( \bigl[1\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{5}{4} a + 6\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a^{2} - \frac{17}{2} a - 2\) , \( -\frac{7}{4} a^{3} - \frac{13}{4} a^{2} + \frac{35}{4} a + 15\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{3}{4}a^{2}+\frac{5}{4}a+6\right){x}^{2}+\left(\frac{1}{2}a^{3}-\frac{3}{2}a^{2}-\frac{17}{2}a-2\right){x}-\frac{7}{4}a^{3}-\frac{13}{4}a^{2}+\frac{35}{4}a+15$ |
| 11.2-b6 |
11.2-b |
$6$ |
$8$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
11.2 |
\( 11 \) |
\( 11^{4} \) |
$10.53010$ |
$(a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$1462.878091$ |
2.094103896 |
\( -\frac{36734695}{58564} a^{3} - \frac{9480475}{5324} a^{2} + \frac{384206015}{58564} a + \frac{309995058}{14641} \) |
\( \bigl[a + 1\) , \( -\frac{1}{4} a^{3} + \frac{1}{4} a^{2} + \frac{1}{4} a + 1\) , \( a^{2} - 5\) , \( -10 a^{3} - 17 a^{2} + 32 a + 50\) , \( \frac{91}{2} a^{3} + \frac{183}{2} a^{2} - \frac{289}{2} a - 252\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-5\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}+\frac{1}{4}a^{2}+\frac{1}{4}a+1\right){x}^{2}+\left(-10a^{3}-17a^{2}+32a+50\right){x}+\frac{91}{2}a^{3}+\frac{183}{2}a^{2}-\frac{289}{2}a-252$ |
| 16.1-a1 |
16.1-a |
$2$ |
$5$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$11.03503$ |
$(1/2a^3-1/2a^2-7/2a+2), (-1/4a^3-3/4a^2+5/4a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 1 \) |
$0.214361144$ |
$243.3553470$ |
2.389610001 |
\( -\frac{21331495}{8} a^{3} + \frac{21331495}{8} a^{2} + \frac{106657475}{8} a - 17271505 \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( a^{2} - 5\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{5}{4} a - 4\) , \( \frac{25}{2} a^{3} + \frac{17}{2} a^{2} - \frac{195}{2} a - 114\) , \( -\frac{231}{4} a^{3} - \frac{165}{4} a^{2} + \frac{1791}{4} a + 536\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{5}{4}a-4\right){y}={x}^{3}+\left(a^{2}-5\right){x}^{2}+\left(\frac{25}{2}a^{3}+\frac{17}{2}a^{2}-\frac{195}{2}a-114\right){x}-\frac{231}{4}a^{3}-\frac{165}{4}a^{2}+\frac{1791}{4}a+536$ |
| 16.1-a2 |
16.1-a |
$2$ |
$5$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$11.03503$ |
$(1/2a^3-1/2a^2-7/2a+2), (-1/4a^3-3/4a^2+5/4a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1[2] |
$1$ |
\( 5 \) |
$0.042872228$ |
$243.3553470$ |
2.389610001 |
\( \frac{22555}{128} a^{3} - \frac{22555}{128} a^{2} - \frac{112775}{128} a + \frac{36665}{32} \) |
\( \bigl[1\) , \( -a^{2} + a + 4\) , \( a\) , \( \frac{1}{4} a^{3} + \frac{11}{4} a^{2} - \frac{5}{4} a - 5\) , \( -\frac{11}{4} a^{3} + \frac{35}{4} a^{2} + \frac{15}{4} a - 18\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(\frac{1}{4}a^{3}+\frac{11}{4}a^{2}-\frac{5}{4}a-5\right){x}-\frac{11}{4}a^{3}+\frac{35}{4}a^{2}+\frac{15}{4}a-18$ |
| 16.1-b1 |
16.1-b |
$4$ |
$15$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$11.03503$ |
$(1/2a^3-1/2a^2-7/2a+2), (-1/4a^3-3/4a^2+5/4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.1[2] |
$1$ |
\( 3^{2} \cdot 5 \) |
$1$ |
$4.127650163$ |
2.127137047 |
\( -\frac{2250604269878421315}{32768} a^{3} + \frac{2642675288363010225}{16384} a^{2} + \frac{1641074714282863715}{4096} a - \frac{834537563842650135}{1024} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 5\) , \( \frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( 1\) , \( -17 a^{3} - 105 a^{2} + 81 a + 259\) , \( -658 a^{3} - 2134 a^{2} + 2392 a + 5492\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-5\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}^{2}+\left(-17a^{3}-105a^{2}+81a+259\right){x}-658a^{3}-2134a^{2}+2392a+5492$ |
| 16.1-b2 |
16.1-b |
$4$ |
$15$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{36} \) |
$11.03503$ |
$(1/2a^3-1/2a^2-7/2a+2), (-1/4a^3-3/4a^2+5/4a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.2, 5B.4.1[2] |
$1$ |
\( 3^{2} \cdot 5 \) |
$1$ |
$4.127650163$ |
2.127137047 |
\( -\frac{1023023601948820745}{32768} a^{3} - \frac{1005861352449389195}{16384} a^{2} + \frac{809885411218325145}{8192} a + \frac{5517837390381990175}{32768} \) |
\( \bigl[\frac{1}{4} a^{3} + \frac{3}{4} a^{2} - \frac{9}{4} a - 4\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{9}{4} a + 1\) , \( 1\) , \( -\frac{97}{2} a^{3} + \frac{339}{2} a^{2} + \frac{495}{2} a - 961\) , \( -\frac{3161}{2} a^{3} + \frac{8745}{2} a^{2} + \frac{17601}{2} a - 23326\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}+\frac{3}{4}a^{2}-\frac{9}{4}a-4\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{9}{4}a+1\right){x}^{2}+\left(-\frac{97}{2}a^{3}+\frac{339}{2}a^{2}+\frac{495}{2}a-961\right){x}-\frac{3161}{2}a^{3}+\frac{8745}{2}a^{2}+\frac{17601}{2}a-23326$ |
| 16.1-b3 |
16.1-b |
$4$ |
$15$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$11.03503$ |
$(1/2a^3-1/2a^2-7/2a+2), (-1/4a^3-3/4a^2+5/4a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.1[2] |
$1$ |
\( 5 \) |
$1$ |
$334.3396632$ |
2.127137047 |
\( \frac{1048510435}{32} a^{3} + \frac{750111075}{32} a^{2} - \frac{1019008935}{4} a - \frac{611790345}{2} \) |
\( \bigl[\frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a + 1\) , \( 1\) , \( \frac{91}{4} a^{3} + \frac{185}{4} a^{2} - \frac{291}{4} a - 126\) , \( 489 a^{3} + 963 a^{2} - 1549 a - 2641\bigr] \) |
${y}^2+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){x}{y}+{y}={x}^{3}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a+1\right){x}^{2}+\left(\frac{91}{4}a^{3}+\frac{185}{4}a^{2}-\frac{291}{4}a-126\right){x}+489a^{3}+963a^{2}-1549a-2641$ |
| 16.1-b4 |
16.1-b |
$4$ |
$15$ |
4.4.7625.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$11.03503$ |
$(1/2a^3-1/2a^2-7/2a+2), (-1/4a^3-3/4a^2+5/4a+2)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3, 5$ |
3B.1.1, 5B.4.1[2] |
$1$ |
\( 5 \) |
$1$ |
$334.3396632$ |
2.127137047 |
\( \frac{3083143945}{128} a^{3} - \frac{10277629985}{128} a^{2} - \frac{3777642505}{128} a + \frac{5288050275}{32} \) |
\( \bigl[a + 1\) , \( -\frac{1}{4} a^{3} - \frac{3}{4} a^{2} + \frac{13}{4} a + 4\) , \( \frac{1}{4} a^{3} - \frac{1}{4} a^{2} - \frac{1}{4} a\) , \( \frac{95}{2} a^{3} - \frac{233}{2} a^{2} - \frac{549}{2} a + 599\) , \( 927 a^{3} - 2184 a^{2} - 5402 a + 11045\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(\frac{1}{4}a^{3}-\frac{1}{4}a^{2}-\frac{1}{4}a\right){y}={x}^{3}+\left(-\frac{1}{4}a^{3}-\frac{3}{4}a^{2}+\frac{13}{4}a+4\right){x}^{2}+\left(\frac{95}{2}a^{3}-\frac{233}{2}a^{2}-\frac{549}{2}a+599\right){x}+927a^{3}-2184a^{2}-5402a+11045$ |
*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.
