| 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 |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{5} \) |
$13.39315$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$175.2883674$ |
1.341680343 |
\( -\frac{39478337}{243} a^{3} + \frac{99456248}{243} a^{2} + \frac{186617770}{243} a - \frac{169310944}{243} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a\) , \( a^{3} - 2 a^{2} - 4 a - 1\) , \( 0\) , \( a^{3} - 2 a^{2} - a + 2\) , \( -23 a^{3} + 63 a^{2} + 78 a - 41\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-4a-1\right){x}^{2}+\left(a^{3}-2a^{2}-a+2\right){x}-23a^{3}+63a^{2}+78a-41$ |
| 3.1-b1 |
3.1-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3 \) |
$13.39315$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$105.6323784$ |
0.808524192 |
\( \frac{23080453}{3} a^{3} - \frac{62543149}{3} a^{2} - \frac{77677631}{3} a + \frac{40420460}{3} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{2} - a - 5\) , \( a^{3} - a^{2} - 7 a - 3\) , \( 2 a^{3} - 2 a^{2} - 14 a - 9\) , \( a^{3} - a^{2} - 8 a - 6\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{3}-a^{2}-7a-3\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(2a^{3}-2a^{2}-14a-9\right){x}+a^{3}-a^{2}-8a-6$ |
| 3.1-b2 |
3.1-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{3} \) |
$13.39315$ |
$(a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$105.6323784$ |
0.808524192 |
\( -\frac{2008670}{27} a^{3} - \frac{5057380}{27} a^{2} - \frac{1758392}{27} a + \frac{1736501}{27} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 5\) , \( a + 1\) , \( -2 a^{3} + a^{2} + 20 a + 21\) , \( 5 a^{3} - 2 a^{2} - 39 a - 36\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-2a^{3}+a^{2}+20a+21\right){x}+5a^{3}-2a^{2}-39a-36$ |
| 3.2-a1 |
3.2-a |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{5} \) |
$13.39315$ |
$(-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$175.2883674$ |
1.341680343 |
\( \frac{11246470}{243} a^{3} - \frac{4776946}{27} a^{2} - \frac{45458435}{243} a + \frac{8303627}{81} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( 80 a^{3} - 47 a^{2} - 660 a - 590\) , \( -14552 a^{3} + 8620 a^{2} + 119930 a + 107096\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(80a^{3}-47a^{2}-660a-590\right){x}-14552a^{3}+8620a^{2}+119930a+107096$ |
| 3.2-b1 |
3.2-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3 \) |
$13.39315$ |
$(-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$105.6323784$ |
0.808524192 |
\( \frac{11658358}{3} a^{3} - 2311491 a^{2} - \frac{96016424}{3} a - 28559112 \) |
\( \bigl[a^{3} - a^{2} - 7 a - 4\) , \( -a^{3} + 3 a^{2} + 4 a - 5\) , \( a^{3} - 2 a^{2} - 4 a\) , \( -a^{3} - a^{2} + 11 a + 17\) , \( -3 a^{3} + 2 a^{2} + 25 a + 17\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a-4\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+4a-5\right){x}^{2}+\left(-a^{3}-a^{2}+11a+17\right){x}-3a^{3}+2a^{2}+25a+17$ |
| 3.2-b2 |
3.2-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{3} \) |
$13.39315$ |
$(-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$105.6323784$ |
0.808524192 |
\( -\frac{41034572}{27} a^{3} + \frac{10127096}{3} a^{2} + \frac{216974602}{27} a - \frac{33604147}{9} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a\) , \( a^{3} - a^{2} - 7 a - 4\) , \( a^{3} - a^{2} - 6 a - 4\) , \( -5 a^{3} + 13 a^{2} + 20 a - 4\) , \( -2 a^{3} + 10 a^{2} - a - 20\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a\right){x}{y}+\left(a^{3}-a^{2}-6a-4\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-4\right){x}^{2}+\left(-5a^{3}+13a^{2}+20a-4\right){x}-2a^{3}+10a^{2}-a-20$ |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$15.36466$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.434077405$ |
$328.6757440$ |
3.276061535 |
\( \frac{16679643524}{27} a^{3} - \frac{5013645460}{3} a^{2} - \frac{56448461584}{27} a + \frac{9792839605}{9} \) |
\( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( -a^{3} + a^{2} + 7 a + 5\) , \( a^{3} - a^{2} - 6 a - 3\) , \( -6 a^{3} - a^{2} + 58 a + 55\) , \( -22 a^{3} + 24 a^{2} + 154 a + 105\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a+5\right){x}^{2}+\left(-6a^{3}-a^{2}+58a+55\right){x}-22a^{3}+24a^{2}+154a+105$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$15.36466$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.217038702$ |
$164.3378720$ |
3.276061535 |
\( -\frac{1477818427379603115196}{729} a^{3} + \frac{445055063225038905106}{81} a^{2} + \frac{4971503066625305022608}{729} a - \frac{864013551541148468249}{243} \) |
\( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( -a^{3} + a^{2} + 7 a + 5\) , \( a^{3} - a^{2} - 6 a - 3\) , \( 44 a^{3} - 136 a^{2} - 112 a + 140\) , \( -340 a^{3} + 890 a^{2} + 1215 a - 470\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a+5\right){x}^{2}+\left(44a^{3}-136a^{2}-112a+140\right){x}-340a^{3}+890a^{2}+1215a-470$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$15.36466$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.072346234$ |
$1479.040848$ |
3.276061535 |
\( \frac{7509168023}{729} a^{3} + \frac{20859415606}{729} a^{2} + \frac{8989900874}{729} a - \frac{6451688741}{729} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 6 a - 1\) , \( 0\) , \( 20 a^{3} - 44 a^{2} - 108 a + 44\) , \( 37 a^{3} - 83 a^{2} - 190 a + 103\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}={x}^{3}+\left(a^{3}-2a^{2}-6a-1\right){x}^{2}+\left(20a^{3}-44a^{2}-108a+44\right){x}+37a^{3}-83a^{2}-190a+103$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$15.36466$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.144692468$ |
$2958.081696$ |
3.276061535 |
\( \frac{30713}{27} a^{3} - \frac{18341}{27} a^{2} - \frac{94933}{27} a + \frac{21478}{27} \) |
\( \bigl[1\) , \( -a + 1\) , \( a^{3} - a^{2} - 7 a - 4\) , \( 4 a^{3} - 2 a^{2} - 34 a - 30\) , \( -20 a^{3} + 12 a^{2} + 164 a + 146\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-7a-4\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a^{3}-2a^{2}-34a-30\right){x}-20a^{3}+12a^{2}+164a+146$ |
| 9.1-b1 |
9.1-b |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$15.36466$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.217038702$ |
$164.3378720$ |
3.276061535 |
\( -\frac{745831354853881921882}{729} a^{3} + \frac{441803995441619928202}{729} a^{2} + \frac{6146745844542120162782}{729} a + \frac{5488957417765283197501}{729} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( a^{3} - 3 a^{2} - 4 a + 4\) , \( a^{3} - a^{2} - 6 a - 3\) , \( 26 a^{3} - 15 a^{2} - 217 a - 199\) , \( -128 a^{3} + 76 a^{2} + 1052 a + 935\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+4\right){x}^{2}+\left(26a^{3}-15a^{2}-217a-199\right){x}-128a^{3}+76a^{2}+1052a+935$ |
| 9.1-b2 |
9.1-b |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$15.36466$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.434077405$ |
$328.6757440$ |
3.276061535 |
\( \frac{8338833284}{27} a^{3} - \frac{4914144476}{27} a^{2} - \frac{68643922456}{27} a - \frac{61306946069}{27} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( a^{3} - 3 a^{2} - 4 a + 4\) , \( a^{3} - a^{2} - 6 a - 3\) , \( a^{3} - 12 a - 14\) , \( -a^{3} + 2 a^{2} + 3 a - 6\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-3\right){y}={x}^{3}+\left(a^{3}-3a^{2}-4a+4\right){x}^{2}+\left(a^{3}-12a-14\right){x}-a^{3}+2a^{2}+3a-6$ |
| 9.1-b3 |
9.1-b |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$15.36466$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$0.072346234$ |
$1479.040848$ |
3.276061535 |
\( \frac{161678163968}{729} a^{3} - \frac{39914897732}{81} a^{2} - \frac{854926560829}{729} a + \frac{132953856256}{243} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a + 1\) , \( a^{3} - 2 a^{2} - 5 a\) , \( 4 a^{2} + 10 a - 5\) , \( 5 a^{3} + 3 a^{2} - 11 a + 3\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a^{2}+10a-5\right){x}+5a^{3}+3a^{2}-11a+3$ |
| 9.1-b4 |
9.1-b |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$15.36466$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.144692468$ |
$2958.081696$ |
3.276061535 |
\( \frac{218600}{27} a^{3} - \frac{53365}{3} a^{2} - \frac{1151632}{27} a + \frac{170320}{9} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a + 1\) , \( a^{3} - 2 a^{2} - 5 a\) , \( -a^{2}\) , \( -a^{2} - a\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+\left(a+1\right){x}^{2}-a^{2}{x}-a^{2}-a$ |
| 9.3-a1 |
9.3-a |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{9} \) |
$15.36466$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.470065248$ |
$65.54022477$ |
3.772958385 |
\( -\frac{2008670}{27} a^{3} - \frac{5057380}{27} a^{2} - \frac{1758392}{27} a + \frac{1736501}{27} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a + 1\) , \( -27 a^{3} - 60 a^{2} - a + 41\) , \( -421 a^{3} - 1057 a^{2} - 357 a + 374\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(-27a^{3}-60a^{2}-a+41\right){x}-421a^{3}-1057a^{2}-357a+374$ |
| 9.3-a2 |
9.3-a |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{7} \) |
$15.36466$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.156688416$ |
$196.6206743$ |
3.772958385 |
\( \frac{23080453}{3} a^{3} - \frac{62543149}{3} a^{2} - \frac{77677631}{3} a + \frac{40420460}{3} \) |
\( \bigl[a + 1\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{3} - 2 a^{2} - 5 a\) , \( 4 a^{3} - 10 a^{2} - 10 a + 12\) , \( -5 a^{3} - 31 a^{2} - 19 a + 14\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+\left(a^{3}-3a^{2}-3a+5\right){x}^{2}+\left(4a^{3}-10a^{2}-10a+12\right){x}-5a^{3}-31a^{2}-19a+14$ |
| 9.3-b1 |
9.3-b |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.3 |
\( 3^{2} \) |
\( 3^{11} \) |
$15.36466$ |
$(a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.043778022$ |
$409.0853411$ |
2.193239194 |
\( -\frac{39478337}{243} a^{3} + \frac{99456248}{243} a^{2} + \frac{186617770}{243} a - \frac{169310944}{243} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 4\) , \( a^{2} - 2 a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - 3 a^{2} + 2 a + 8\) , \( -32 a^{3} + 88 a^{2} + 113 a - 52\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-4\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(a^{3}-3a^{2}+2a+8\right){x}-32a^{3}+88a^{2}+113a-52$ |
| 9.4-a1 |
9.4-a |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{9} \) |
$15.36466$ |
$(-a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.470065248$ |
$65.54022477$ |
3.772958385 |
\( -\frac{41034572}{27} a^{3} + \frac{10127096}{3} a^{2} + \frac{216974602}{27} a - \frac{33604147}{9} \) |
\( \bigl[a^{2} - a - 4\) , \( a^{2} - 2 a - 3\) , \( a^{2} - a - 3\) , \( -a^{3} + 9 a^{2} - 6 a - 38\) , \( 75 a^{3} - 30 a^{2} - 642 a - 634\bigr] \) |
${y}^2+\left(a^{2}-a-4\right){x}{y}+\left(a^{2}-a-3\right){y}={x}^{3}+\left(a^{2}-2a-3\right){x}^{2}+\left(-a^{3}+9a^{2}-6a-38\right){x}+75a^{3}-30a^{2}-642a-634$ |
| 9.4-a2 |
9.4-a |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{7} \) |
$15.36466$ |
$(-a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.156688416$ |
$196.6206743$ |
3.772958385 |
\( \frac{11658358}{3} a^{3} - 2311491 a^{2} - \frac{96016424}{3} a - 28559112 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{2} - 2 a - 3\) , \( 4 a^{3} - 3 a^{2} - 31 a - 7\) , \( -181 a^{3} + 416 a^{2} + 936 a - 518\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+6a+1\right){x}^{2}+\left(4a^{3}-3a^{2}-31a-7\right){x}-181a^{3}+416a^{2}+936a-518$ |
| 9.4-b1 |
9.4-b |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
9.4 |
\( 3^{2} \) |
\( 3^{11} \) |
$15.36466$ |
$(-a^2+2a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.043778022$ |
$409.0853411$ |
2.193239194 |
\( \frac{11246470}{243} a^{3} - \frac{4776946}{27} a^{2} - \frac{45458435}{243} a + \frac{8303627}{81} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 3\) , \( -a^{3} + 2 a^{2} + 6 a - 1\) , \( 0\) , \( a^{2} + 11 a + 15\) , \( -16 a^{3} + 14 a^{2} + 143 a + 124\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-3\right){x}{y}={x}^{3}+\left(-a^{3}+2a^{2}+6a-1\right){x}^{2}+\left(a^{2}+11a+15\right){x}-16a^{3}+14a^{2}+143a+124$ |
| 16.1-a1 |
16.1-a |
$6$ |
$45$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$16.51040$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.1 |
$1$ |
\( 3 \) |
$0.675817085$ |
$815.4744629$ |
2.024774817 |
\( \frac{1331}{8} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a + 1\) , \( -a^{3} + 2 a^{2} + 5 a + 1\) , \( 1\) , \( -a^{3} + 2 a^{2} + 5 a + 3\) , \( a^{3} - 2 a^{2} - 5 a + 4\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+5a+1\right){x}^{2}+\left(-a^{3}+2a^{2}+5a+3\right){x}+a^{3}-2a^{2}-5a+4$ |
| 16.1-a2 |
16.1-a |
$6$ |
$45$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{60} \) |
$16.51040$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3Cs, 5B.1.2 |
$1$ |
\( 3 \cdot 5 \) |
$3.379085427$ |
$1.304759140$ |
2.024774817 |
\( -\frac{1680914269}{32768} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a + 1\) , \( -a^{3} + 2 a^{2} + 5 a + 1\) , \( 1\) , \( -76 a^{3} + 152 a^{2} + 380 a - 172\) , \( -507 a^{3} + 1014 a^{2} + 2535 a - 1170\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+5a+1\right){x}^{2}+\left(-76a^{3}+152a^{2}+380a-172\right){x}-507a^{3}+1014a^{2}+2535a-1170$ |
| 16.1-a3 |
16.1-a |
$6$ |
$45$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.51040$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$2.027451256$ |
$815.4744629$ |
2.024774817 |
\( -\frac{461373}{2} a^{3} + 461373 a^{2} + \frac{2306865}{2} a - 531398 \) |
\( \bigl[1\) , \( 1\) , \( a^{3} - 2 a^{2} - 5 a\) , \( -2 a^{3} + 4 a^{2} + 10 a - 3\) , \( a^{3} - 2 a^{2} - 5 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+{x}^{2}+\left(-2a^{3}+4a^{2}+10a-3\right){x}+a^{3}-2a^{2}-5a+1$ |
| 16.1-a4 |
16.1-a |
$6$ |
$45$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$16.51040$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 5 \) |
$10.13725628$ |
$1.304759140$ |
2.024774817 |
\( \frac{1250637664527933}{32} a^{3} - \frac{1250637664527933}{16} a^{2} - \frac{6253188322639665}{32} a - \frac{1629300280935823}{32} \) |
\( \bigl[1\) , \( 1\) , \( a^{3} - 2 a^{2} - 5 a\) , \( 28 a^{3} - 56 a^{2} - 140 a + 2\) , \( 52 a^{3} - 104 a^{2} - 260 a - 106\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+{x}^{2}+\left(28a^{3}-56a^{2}-140a+2\right){x}+52a^{3}-104a^{2}-260a-106$ |
| 16.1-a5 |
16.1-a |
$6$ |
$45$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$16.51040$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 5 \) |
$10.13725628$ |
$1.304759140$ |
2.024774817 |
\( -\frac{1250637664527933}{32} a^{3} + \frac{1250637664527933}{16} a^{2} + \frac{6253188322639665}{32} a - \frac{719984486365939}{8} \) |
\( \bigl[1\) , \( 1\) , \( a^{3} - 2 a^{2} - 5 a + 1\) , \( -29 a^{3} + 58 a^{2} + 145 a - 27\) , \( -52 a^{3} + 104 a^{2} + 260 a - 158\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-5a+1\right){y}={x}^{3}+{x}^{2}+\left(-29a^{3}+58a^{2}+145a-27\right){x}-52a^{3}+104a^{2}+260a-158$ |
| 16.1-a6 |
16.1-a |
$6$ |
$45$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.51040$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$2.027451256$ |
$815.4744629$ |
2.024774817 |
\( \frac{461373}{2} a^{3} - 461373 a^{2} - \frac{2306865}{2} a - \frac{601423}{2} \) |
\( \bigl[1\) , \( 1\) , \( a^{3} - 2 a^{2} - 5 a + 1\) , \( a^{3} - 2 a^{2} - 5 a - 2\) , \( -a^{3} + 2 a^{2} + 5 a\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a^{2}-5a+1\right){y}={x}^{3}+{x}^{2}+\left(a^{3}-2a^{2}-5a-2\right){x}-a^{3}+2a^{2}+5a$ |
| 17.1-a1 |
17.1-a |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$16.63599$ |
$(a^3-3a^2-4a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.182277881$ |
$632.7150580$ |
3.531003071 |
\( \frac{4828831}{17} a^{3} - \frac{2896367}{17} a^{2} - \frac{39714711}{17} a - \frac{35384193}{17} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 3\) , \( a\) , \( a^{3} - 2 a^{2} - 5 a + 1\) , \( -a^{3} + 4 a^{2} + 16 a + 11\) , \( 6 a^{2} + 17 a + 11\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-3\right){x}{y}+\left(a^{3}-2a^{2}-5a+1\right){y}={x}^{3}+a{x}^{2}+\left(-a^{3}+4a^{2}+16a+11\right){x}+6a^{2}+17a+11$ |
| 17.1-b1 |
17.1-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17 \) |
$16.63599$ |
$(a^3-3a^2-4a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.023323421$ |
$2556.652764$ |
1.825660249 |
\( -\frac{4882}{17} a^{3} + \frac{19817}{17} a^{2} + \frac{13843}{17} a - \frac{21712}{17} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 3\) , \( a^{2} - 2 a - 4\) , \( a^{2} - 2 a - 3\) , \( a^{3} + 3 a^{2} - 4 a - 8\) , \( 2 a^{3} + 2 a^{2} - 2 a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-3\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(a^{2}-2a-4\right){x}^{2}+\left(a^{3}+3a^{2}-4a-8\right){x}+2a^{3}+2a^{2}-2a-2$ |
| 17.1-b2 |
17.1-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.1 |
\( 17 \) |
\( 17^{3} \) |
$16.63599$ |
$(a^3-3a^2-4a+8)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.069970264$ |
$284.0725293$ |
1.825660249 |
\( -\frac{14216793170}{4913} a^{3} + \frac{39622932371}{4913} a^{2} + \frac{48714472133}{4913} a - \frac{25475916001}{4913} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a + 1\) , \( 1\) , \( 4 a^{3} - 11 a^{2} - 15 a + 12\) , \( -20 a^{3} + 45 a^{2} + 103 a - 47\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a+1\right){x}^{2}+\left(4a^{3}-11a^{2}-15a+12\right){x}-20a^{3}+45a^{2}+103a-47$ |
| 17.2-a1 |
17.2-a |
$2$ |
$2$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( - 17^{2} \) |
$16.63599$ |
$(2a^3-4a^2-11a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$244.3408590$ |
0.935108622 |
\( \frac{1555934441411}{289} a^{3} - \frac{3340663859720}{289} a^{2} - \frac{8077737100087}{289} a + \frac{3742495543803}{289} \) |
\( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 5 a\) , \( -6 a^{3} + 23 a^{2} + 19 a - 64\) , \( -34 a^{3} + 68 a^{2} + 200 a - 33\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a-3\right){x}{y}+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-6a^{3}+23a^{2}+19a-64\right){x}-34a^{3}+68a^{2}+200a-33$ |
| 17.2-a2 |
17.2-a |
$2$ |
$2$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$16.63599$ |
$(2a^3-4a^2-11a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$488.6817180$ |
0.935108622 |
\( -\frac{1405579}{17} a^{3} + \frac{3593410}{17} a^{2} + \frac{6022615}{17} a - \frac{2956764}{17} \) |
\( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 5 a\) , \( -a^{3} + 3 a^{2} + 9 a + 1\) , \( -a^{3} + a^{2} + 14 a + 11\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a-3\right){x}{y}+\left(a^{3}-2a^{2}-5a\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{3}+3a^{2}+9a+1\right){x}-a^{3}+a^{2}+14a+11$ |
| 17.2-b1 |
17.2-b |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.2 |
\( 17 \) |
\( 17 \) |
$16.63599$ |
$(2a^3-4a^2-11a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.071860716$ |
$1427.519210$ |
3.140721722 |
\( -\frac{152}{17} a^{3} + \frac{4819}{17} a^{2} - \frac{9762}{17} a - \frac{18944}{17} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 3\) , \( -a^{3} + a^{2} + 7 a + 5\) , \( a^{3} - a^{2} - 6 a - 4\) , \( -5 a^{3} + 3 a^{2} + 45 a + 43\) , \( -9 a^{3} + 4 a^{2} + 85 a + 88\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-4\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a+5\right){x}^{2}+\left(-5a^{3}+3a^{2}+45a+43\right){x}-9a^{3}+4a^{2}+85a+88$ |
| 17.3-a1 |
17.3-a |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( 17 \) |
$16.63599$ |
$(-a^3+3a^2+2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.182277881$ |
$632.7150580$ |
3.531003071 |
\( \frac{9542160}{17} a^{3} - \frac{25845615}{17} a^{2} - \frac{32140244}{17} a + \frac{16658201}{17} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 4\) , \( a^{3} - a^{2} - 7 a - 3\) , \( a\) , \( -2 a^{3} + 6 a^{2} + 17 a + 1\) , \( 7 a^{3} - 11 a^{2} - 29 a + 17\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-4\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-a^{2}-7a-3\right){x}^{2}+\left(-2a^{3}+6a^{2}+17a+1\right){x}+7a^{3}-11a^{2}-29a+17$ |
| 17.3-b1 |
17.3-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( 17 \) |
$16.63599$ |
$(-a^3+3a^2+2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.023323421$ |
$2556.652764$ |
1.825660249 |
\( \frac{14710}{17} a^{3} - \frac{39473}{17} a^{2} - \frac{62983}{17} a + \frac{68251}{17} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( a^{2} - a - 4\) , \( -a^{3} + 4 a^{2} + 12 a + 6\) , \( -a^{3} + 6 a^{2} + 18 a + 11\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-4\right){x}{y}+\left(a^{2}-a-4\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a\right){x}^{2}+\left(-a^{3}+4a^{2}+12a+6\right){x}-a^{3}+6a^{2}+18a+11$ |
| 17.3-b2 |
17.3-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.3 |
\( 17 \) |
\( 17^{3} \) |
$16.63599$ |
$(-a^3+3a^2+2a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.069970264$ |
$284.0725293$ |
1.825660249 |
\( -\frac{3018248794}{4913} a^{3} - \frac{5152848443}{4913} a^{2} + \frac{37460737687}{4913} a + \frac{64048050592}{4913} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a + 1\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 278 a^{3} - 166 a^{2} - 2287 a - 2039\) , \( -5572 a^{3} + 3299 a^{2} + 45925 a + 41014\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(278a^{3}-166a^{2}-2287a-2039\right){x}-5572a^{3}+3299a^{2}+45925a+41014$ |
| 17.4-a1 |
17.4-a |
$2$ |
$2$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( 17 \) |
$16.63599$ |
$(-a^3+2a^2+4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$488.6817180$ |
0.935108622 |
\( -\frac{64103}{17} a^{3} - \frac{654046}{17} a^{2} + \frac{1325795}{17} a + \frac{3860476}{17} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 6 a - 4\) , \( -2 a^{3} + 5 a^{2} + 7 a - 2\) , \( -2 a^{3} + 6 a^{2} + 3 a - 9\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+6a+1\right){x}^{2}+\left(-2a^{3}+5a^{2}+7a-2\right){x}-2a^{3}+6a^{2}+3a-9$ |
| 17.4-a2 |
17.4-a |
$2$ |
$2$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( - 17^{2} \) |
$16.63599$ |
$(-a^3+2a^2+4a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$244.3408590$ |
0.935108622 |
\( \frac{571484617685}{289} a^{3} - \frac{914174258472}{289} a^{2} - \frac{2559358195393}{289} a + \frac{1156480881791}{289} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 6 a - 4\) , \( 8 a^{3} - 25 a^{2} - 28 a + 18\) , \( -16 a^{3} + 33 a^{2} + 42 a - 27\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+\left(a^{3}-a^{2}-6a-4\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+6a+1\right){x}^{2}+\left(8a^{3}-25a^{2}-28a+18\right){x}-16a^{3}+33a^{2}+42a-27$ |
| 17.4-b1 |
17.4-b |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
17.4 |
\( 17 \) |
\( 17 \) |
$16.63599$ |
$(-a^3+2a^2+4a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.071860716$ |
$1427.519210$ |
3.140721722 |
\( \frac{2871}{17} a^{3} - \frac{10257}{17} a^{2} - \frac{3833}{17} a + \frac{15684}{17} \) |
\( \bigl[a^{3} - a^{2} - 6 a - 4\) , \( a^{3} - 3 a^{2} - 2 a + 5\) , \( a + 1\) , \( -7 a^{3} + 8 a^{2} + 60 a + 49\) , \( -9 a^{3} + 10 a^{2} + 87 a + 75\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a-4\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-3a^{2}-2a+5\right){x}^{2}+\left(-7a^{3}+8a^{2}+60a+49\right){x}-9a^{3}+10a^{2}+87a+75$ |
| 27.3-a1 |
27.3-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( - 3^{14} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$367.1200803$ |
1.873323760 |
\( \frac{161678163968}{729} a^{3} - \frac{39914897732}{81} a^{2} - \frac{854926560829}{729} a + \frac{132953856256}{243} \) |
\( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( 0\) , \( a^{3} - a^{2} - 7 a - 3\) , \( 4 a^{3} - 4 a^{2} - 28 a - 27\) , \( 21 a^{3} - 8 a^{2} - 183 a - 173\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a-3\right){x}{y}+\left(a^{3}-a^{2}-7a-3\right){y}={x}^{3}+\left(4a^{3}-4a^{2}-28a-27\right){x}+21a^{3}-8a^{2}-183a-173$ |
| 27.3-a2 |
27.3-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{10} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$734.2401607$ |
1.873323760 |
\( \frac{218600}{27} a^{3} - \frac{53365}{3} a^{2} - \frac{1151632}{27} a + \frac{170320}{9} \) |
\( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( 0\) , \( a^{3} - a^{2} - 7 a - 3\) , \( -a^{3} + a^{2} + 7 a + 3\) , \( -a^{3} + a^{2} + 7 a + 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a-3\right){x}{y}+\left(a^{3}-a^{2}-7a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a+3\right){x}-a^{3}+a^{2}+7a+4$ |
| 27.3-a3 |
27.3-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{10} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{2} \) |
$1$ |
$27.19408002$ |
1.873323760 |
\( \frac{8338833284}{27} a^{3} - \frac{4914144476}{27} a^{2} - \frac{68643922456}{27} a - \frac{61306946069}{27} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 8 a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -61 a^{3} + 149 a^{2} + 201 a - 86\) , \( 491 a^{3} - 1435 a^{2} - 1745 a + 903\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-8a-4\right){x}^{2}+\left(-61a^{3}+149a^{2}+201a-86\right){x}+491a^{3}-1435a^{2}-1745a+903$ |
| 27.3-a4 |
27.3-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( - 3^{14} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2^{3} \) |
$1$ |
$13.59704001$ |
1.873323760 |
\( -\frac{745831354853881921882}{729} a^{3} + \frac{441803995441619928202}{729} a^{2} + \frac{6146745844542120162782}{729} a + \frac{5488957417765283197501}{729} \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 8 a - 4\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( 419 a^{3} - 1151 a^{2} - 1414 a + 754\) , \( 6753 a^{3} - 18414 a^{2} - 22814 a + 11892\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-8a-4\right){x}^{2}+\left(419a^{3}-1151a^{2}-1414a+754\right){x}+6753a^{3}-18414a^{2}-22814a+11892$ |
| 27.3-b1 |
27.3-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{9} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$113.5428812$ |
2.607216680 |
\( -\frac{41034572}{27} a^{3} + \frac{10127096}{3} a^{2} + \frac{216974602}{27} a - \frac{33604147}{9} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( -a^{3} + a^{2} + 6 a + 3\) , \( a\) , \( -9 a^{3} + 17 a^{2} + 53 a + 3\) , \( -11 a^{3} + 20 a^{2} + 64 a - 3\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+a^{2}+6a+3\right){x}^{2}+\left(-9a^{3}+17a^{2}+53a+3\right){x}-11a^{3}+20a^{2}+64a-3$ |
| 27.3-b2 |
27.3-b |
$2$ |
$3$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{7} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$340.6286436$ |
2.607216680 |
\( \frac{11658358}{3} a^{3} - 2311491 a^{2} - \frac{96016424}{3} a - 28559112 \) |
\( \bigl[a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{2} + 2 a + 5\) , \( a^{3} - 2 a^{2} - 5 a + 1\) , \( a^{3} - a^{2} - 4 a - 2\) , \( a^{2} + 2 a - 1\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-4a+1\right){x}{y}+\left(a^{3}-2a^{2}-5a+1\right){y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(a^{3}-a^{2}-4a-2\right){x}+a^{2}+2a-1$ |
| 27.3-c1 |
27.3-c |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{10} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.823928050$ |
$250.0786076$ |
3.154218595 |
\( \frac{16679643524}{27} a^{3} - \frac{5013645460}{3} a^{2} - \frac{56448461584}{27} a + \frac{9792839605}{9} \) |
\( \bigl[a^{2} - 2 a - 4\) , \( -a^{3} + 3 a^{2} + 3 a - 4\) , \( a^{2} - 2 a - 4\) , \( -15 a^{3} + 4 a^{2} + 135 a + 130\) , \( -163 a^{3} + 98 a^{2} + 1340 a + 1193\bigr] \) |
${y}^2+\left(a^{2}-2a-4\right){x}{y}+\left(a^{2}-2a-4\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-4\right){x}^{2}+\left(-15a^{3}+4a^{2}+135a+130\right){x}-163a^{3}+98a^{2}+1340a+1193$ |
| 27.3-c2 |
27.3-c |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{10} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.274642683$ |
$750.2358228$ |
3.154218595 |
\( \frac{30713}{27} a^{3} - \frac{18341}{27} a^{2} - \frac{94933}{27} a + \frac{21478}{27} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a + 1\) , \( a^{3} - a^{2} - 7 a - 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( -4 a^{2} + 4 a + 12\) , \( a^{3} - 8 a - 8\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-4\right){x}^{2}+\left(-4a^{2}+4a+12\right){x}+a^{3}-8a-8$ |
| 27.3-c3 |
27.3-c |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( - 3^{14} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.137321341$ |
$375.1179114$ |
3.154218595 |
\( \frac{7509168023}{729} a^{3} + \frac{20859415606}{729} a^{2} + \frac{8989900874}{729} a - \frac{6451688741}{729} \) |
\( \bigl[a^{3} - 2 a^{2} - 5 a + 1\) , \( a^{3} - a^{2} - 7 a - 4\) , \( a^{3} - 2 a^{2} - 4 a\) , \( 10 a^{3} - 54 a^{2} - 51 a + 42\) , \( -13 a^{3} + 190 a^{2} + 160 a - 107\bigr] \) |
${y}^2+\left(a^{3}-2a^{2}-5a+1\right){x}{y}+\left(a^{3}-2a^{2}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-7a-4\right){x}^{2}+\left(10a^{3}-54a^{2}-51a+42\right){x}-13a^{3}+190a^{2}+160a-107$ |
| 27.3-c4 |
27.3-c |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( - 3^{14} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$0.411964025$ |
$125.0393038$ |
3.154218595 |
\( -\frac{1477818427379603115196}{729} a^{3} + \frac{445055063225038905106}{81} a^{2} + \frac{4971503066625305022608}{729} a - \frac{864013551541148468249}{243} \) |
\( \bigl[a + 1\) , \( -a^{3} + 3 a^{2} + 3 a - 4\) , \( a^{2} - 2 a - 3\) , \( -66 a^{3} + 147 a^{2} + 343 a - 168\) , \( -444 a^{3} + 982 a^{2} + 2351 a - 1075\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-3\right){y}={x}^{3}+\left(-a^{3}+3a^{2}+3a-4\right){x}^{2}+\left(-66a^{3}+147a^{2}+343a-168\right){x}-444a^{3}+982a^{2}+2351a-1075$ |
| 27.3-d1 |
27.3-d |
$1$ |
$1$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.3 |
\( 3^{3} \) |
\( 3^{11} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 5 \) |
$1$ |
$54.90959791$ |
2.101426616 |
\( \frac{11246470}{243} a^{3} - \frac{4776946}{27} a^{2} - \frac{45458435}{243} a + \frac{8303627}{81} \) |
\( \bigl[a^{2} - a - 3\) , \( -a^{3} + 3 a^{2} + 2 a - 3\) , \( a\) , \( -5 a^{3} + 9 a^{2} + 14 a - 6\) , \( -7 a^{3} - 4 a^{2} + 5 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+3a^{2}+2a-3\right){x}^{2}+\left(-5a^{3}+9a^{2}+14a-6\right){x}-7a^{3}-4a^{2}+5a-1$ |
| 27.4-a1 |
27.4-a |
$4$ |
$6$ |
4.4.17069.1 |
$4$ |
$[4, 0]$ |
27.4 |
\( 3^{3} \) |
\( 3^{10} \) |
$17.62638$ |
$(a), (-a^2+2a+5)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$734.2401607$ |
1.873323760 |
\( \frac{30713}{27} a^{3} - \frac{18341}{27} a^{2} - \frac{94933}{27} a + \frac{21478}{27} \) |
\( \bigl[a^{2} - 2 a - 3\) , \( a^{2} - 3 a - 5\) , \( 0\) , \( -2 a^{3} + 5 a^{2} + 8 a - 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2a-3\right){x}{y}={x}^{3}+\left(a^{2}-3a-5\right){x}^{2}+\left(-2a^{3}+5a^{2}+8a-2\right){x}$ |
*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.
