| 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 |
$4$ |
$6$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$4.37322$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.289236295$ |
$212.5029006$ |
2.114549490 |
\( \frac{316143}{64} a^{2} + \frac{935109}{64} a + \frac{622997}{64} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( -a^{2} + a + 6\) , \( a^{2} - a - 5\) , \( -19426056 a^{2} - 52714237 a - 20924294\) , \( 163538366356 a^{2} + 443775202583 a + 176151488410\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-19426056a^{2}-52714237a-20924294\right){x}+163538366356a^{2}+443775202583a+176151488410$ |
| 2.1-a2 |
2.1-a |
$4$ |
$6$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{2} \) |
$4.37322$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.867708887$ |
$70.83430023$ |
2.114549490 |
\( -\frac{15011063205}{4} a^{2} + \frac{22259319021}{4} a + \frac{124351464917}{4} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( -a^{2} + a + 6\) , \( a^{2} - a - 5\) , \( -6 a^{2} + 16 a + 24\) , \( 4 a^{2} - 17 a\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(-a^{2}+a+6\right){x}^{2}+\left(-6a^{2}+16a+24\right){x}+4a^{2}-17a$ |
| 2.1-a3 |
2.1-a |
$4$ |
$6$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{3} \) |
$4.37322$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$0.578472591$ |
$212.5029006$ |
2.114549490 |
\( \frac{567}{8} a^{2} - \frac{3195}{8} a + \frac{3925}{8} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 5\) , \( a\) , \( -457389078 a^{2} - 1241163986 a - 492665836\) , \( 202232100651116 a^{2} + 548773926464843 a + 217829530294564\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-457389078a^{2}-1241163986a-492665836\right){x}+202232100651116a^{2}+548773926464843a+217829530294564$ |
| 2.1-a4 |
2.1-a |
$4$ |
$6$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2 \) |
$4.37322$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1.735417774$ |
$70.83430023$ |
2.114549490 |
\( \frac{39949635}{2} a^{2} - \frac{128987577}{2} a - \frac{71927555}{2} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 5\) , \( a\) , \( 4\) , \( -3 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+4{x}-3a^{2}-6a-2$ |
| 2.1-b1 |
2.1-b |
$2$ |
$2$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{10} \) |
$4.37322$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.679014128$ |
$48.56620712$ |
1.134522725 |
\( \frac{154496816367}{1024} a^{2} + \frac{636480072837}{1024} a + \frac{640246034069}{1024} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( -a^{2} + a + 5\) , \( a\) , \( 142 a^{2} + 219 a - 2767\) , \( -12012 a^{2} + 26570 a + 66977\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(142a^{2}+219a-2767\right){x}-12012a^{2}+26570a+66977$ |
| 2.1-b2 |
2.1-b |
$2$ |
$2$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( 2^{5} \) |
$4.37322$ |
$(a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1.358028257$ |
$48.56620712$ |
1.134522725 |
\( \frac{340690345844271}{32} a^{2} - \frac{1100676962253915}{32} a - \frac{610905031498475}{32} \) |
\( \bigl[a + 1\) , \( a^{2} - 2 a - 5\) , \( a\) , \( 127 a^{2} - 187 a - 1050\) , \( -1729 a^{2} + 2568 a + 14316\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(127a^{2}-187a-1050\right){x}-1729a^{2}+2568a+14316$ |
| 2.1-c1 |
2.1-c |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{6} \) |
$4.37322$ |
$(a+2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.641364075$ |
$95.27858406$ |
0.934367249 |
\( -\frac{122119}{64} a^{2} + \frac{244019}{64} a + \frac{256163}{64} \) |
\( \bigl[1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - a - 5\) , \( -708 a^{2} - 1918 a - 752\) , \( -39928 a^{2} - 108353 a - 43018\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(-708a^{2}-1918a-752\right){x}-39928a^{2}-108353a-43018$ |
| 2.1-c2 |
2.1-c |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
2.1 |
\( 2 \) |
\( - 2^{18} \) |
$4.37322$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1.924092227$ |
$3.528836446$ |
0.934367249 |
\( -\frac{7345147908288439}{262144} a^{2} - \frac{19931682374081821}{262144} a - \frac{7911655846417069}{262144} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - a - 6\) , \( 40 a^{2} - 103 a - 156\) , \( 38 a^{2} - 30 a - 396\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(40a^{2}-103a-156\right){x}+38a^{2}-30a-396$ |
| 4.2-a1 |
4.2-a |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
4.2 |
\( 2^{2} \) |
\( - 2^{8} \) |
$4.90877$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$70.33474489$ |
1.613165250 |
\( -255106 a^{2} - 693629 a - 278548 \) |
\( \bigl[a^{2} - 2 a - 6\) , \( 0\) , \( a^{2} - a - 6\) , \( -2\) , \( -a - 1\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-2{x}-a-1$ |
| 6.1-a1 |
6.1-a |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2 \cdot 3^{5} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$146.0563268$ |
3.349880508 |
\( -\frac{923495599}{486} a^{2} - \frac{2507656645}{486} a - \frac{998636501}{486} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 7\) , \( a^{2} - 2 a - 5\) , \( -53569598 a^{2} - 145365619 a - 57701186\) , \( 753685819695 a^{2} + 2045190280222 a + 811814877939\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-53569598a^{2}-145365619a-57701186\right){x}+753685819695a^{2}+2045190280222a+811814877939$ |
| 6.1-a2 |
6.1-a |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{3} \cdot 3^{15} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$48.68544226$ |
3.349880508 |
\( -\frac{22119979375}{114791256} a^{2} + \frac{26235622907}{114791256} a + \frac{205906981867}{114791256} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + a + 7\) , \( a^{2} - 2 a - 5\) , \( -485 a^{2} + 720 a + 4015\) , \( 818 a^{2} - 1212 a - 6779\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(-a^{2}+a+7\right){x}^{2}+\left(-485a^{2}+720a+4015\right){x}+818a^{2}-1212a-6779$ |
| 6.1-b1 |
6.1-b |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{13} \cdot 3^{3} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$34.13039191$ |
2.348396754 |
\( -\frac{22965079}{221184} a^{2} + \frac{74185475}{221184} a + \frac{41131891}{221184} \) |
\( \bigl[a^{2} - a - 5\) , \( -a^{2} + 3 a + 5\) , \( a\) , \( -a^{2} + 2 a + 21\) , \( 14 a + 25\bigr] \) |
${y}^2+\left(a^{2}-a-5\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-a^{2}+2a+21\right){x}+14a+25$ |
| 6.1-c1 |
6.1-c |
$8$ |
$12$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{3} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$48.13330978$ |
1.655945070 |
\( -\frac{153535495015}{1728} a^{2} + \frac{227671626131}{1728} a + \frac{1271889103939}{1728} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a^{2} - 3 a - 6\) , \( 0\) , \( 50 a^{2} - 137 a - 178\) , \( 240 a^{2} - 689 a - 752\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}={x}^{3}+\left(a^{2}-3a-6\right){x}^{2}+\left(50a^{2}-137a-178\right){x}+240a^{2}-689a-752$ |
| 6.1-c2 |
6.1-c |
$8$ |
$12$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$144.3999293$ |
1.655945070 |
\( -\frac{1437277971683}{768} a^{2} + \frac{2131280078335}{768} a + \frac{11906396437295}{768} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a - 1\) , \( a + 1\) , \( -23388482 a^{2} + 75561763 a + 41938793\) , \( -121307480775 a^{2} + 391911162199 a + 217521133703\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-23388482a^{2}+75561763a+41938793\right){x}-121307480775a^{2}+391911162199a+217521133703$ |
| 6.1-c3 |
6.1-c |
$8$ |
$12$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{12} \cdot 3^{6} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$48.13330978$ |
1.655945070 |
\( \frac{95820036767}{2985984} a^{2} + \frac{301685160725}{2985984} a + \frac{201803536933}{2985984} \) |
\( \bigl[1\) , \( a^{2} - a - 7\) , \( a + 1\) , \( -48408 a^{2} + 156395 a + 86796\) , \( 3849633 a^{2} - 12437108 a - 6902927\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-48408a^{2}+156395a+86796\right){x}+3849633a^{2}-12437108a-6902927$ |
| 6.1-c4 |
6.1-c |
$8$ |
$12$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{6} \cdot 3^{12} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$6.016663722$ |
1.655945070 |
\( \frac{1066906435920701525}{34012224} a^{2} + \frac{2895138778208608295}{34012224} a + \frac{1149192022492749463}{34012224} \) |
\( \bigl[1\) , \( a^{2} - a - 7\) , \( a + 1\) , \( -445553 a^{2} + 1439455 a + 798956\) , \( -366163530 a^{2} + 1182973857 a + 656581861\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-445553a^{2}+1439455a+798956\right){x}-366163530a^{2}+1182973857a+656581861$ |
| 6.1-c5 |
6.1-c |
$8$ |
$12$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3 \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$144.3999293$ |
1.655945070 |
\( \frac{15657989}{12} a^{2} + \frac{42538787}{12} a + \frac{16911955}{12} \) |
\( \bigl[1\) , \( a - 1\) , \( a^{2} - a - 5\) , \( -11 a^{2} + 35 a + 22\) , \( -40 a^{2} + 129 a + 67\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-a-5\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a^{2}+35a+22\right){x}-40a^{2}+129a+67$ |
| 6.1-c6 |
6.1-c |
$8$ |
$12$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2Cs, 3B |
$1$ |
\( 2^{3} \) |
$1$ |
$144.3999293$ |
1.655945070 |
\( \frac{505898783}{144} a^{2} - \frac{1638243451}{144} a - \frac{892014203}{144} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( 0\) , \( -63750 a^{2} + 205964 a + 114324\) , \( -20003049 a^{2} + 64624368 a + 35868240\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-63750a^{2}+205964a+114324\right){x}-20003049a^{2}+64624368a+35868240$ |
| 6.1-c7 |
6.1-c |
$8$ |
$12$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{4} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$4$ |
\( 2^{2} \) |
$1$ |
$18.04999116$ |
1.655945070 |
\( \frac{41921863046677025}{324} a^{2} - \frac{135438028744447585}{324} a - \frac{75171713389575617}{324} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( 0\) , \( -1019995 a^{2} + 3295329 a + 1829004\) , \( -1278595581 a^{2} + 4130791259 a + 2292699168\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a^{2}-a-6\right){x}^{2}+\left(-1019995a^{2}+3295329a+1829004\right){x}-1278595581a^{2}+4130791259a+2292699168$ |
| 6.1-c8 |
6.1-c |
$8$ |
$12$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{24} \cdot 3^{3} \) |
$5.25196$ |
$(a+2), (a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$48.13330978$ |
1.655945070 |
\( \frac{34962015775141}{452984832} a^{2} - \frac{113342027752745}{452984832} a - \frac{61419140115577}{452984832} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( -215267539 a^{2} + 695470318 a + 386004541\) , \( 3914441617751 a^{2} - 12646486053255 a - 7019136602855\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-215267539a^{2}+695470318a+386004541\right){x}+3914441617751a^{2}-12646486053255a-7019136602855$ |
| 8.1-a1 |
8.1-a |
$4$ |
$4$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{24} \) |
$5.50991$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.731133283$ |
$17.36219643$ |
2.068070635 |
\( \frac{2584300106223}{1048576} a^{2} + \frac{7031178368901}{1048576} a + \frac{2811525673365}{1048576} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( -1\) , \( 0\) , \( -3320 a^{2} + 10725 a + 5955\) , \( -257368 a^{2} + 831485 a + 461497\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}={x}^{3}-{x}^{2}+\left(-3320a^{2}+10725a+5955\right){x}-257368a^{2}+831485a+461497$ |
| 8.1-a2 |
8.1-a |
$4$ |
$4$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{9} \) |
$5.50991$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$6.924533132$ |
$8.681098219$ |
2.068070635 |
\( \frac{98964267797053521}{32} a^{2} - \frac{319726376070414093}{32} a - \frac{177456654390894453}{32} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -661953807 a^{2} - 1796267698 a - 713007907\) , \( 28686114293093 a^{2} + 77842199754419 a + 30898570416477\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-661953807a^{2}-1796267698a-713007907\right){x}+28686114293093a^{2}+77842199754419a+30898570416477$ |
| 8.1-a3 |
8.1-a |
$4$ |
$4$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$5.50991$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$3.462266566$ |
$34.72439287$ |
2.068070635 |
\( \frac{17666719407}{1024} a^{2} - \frac{57075208443}{1024} a - \frac{31674180843}{1024} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -170786187 a^{2} - 463442778 a - 183958307\) , \( -3836261696323 a^{2} - 10410020898065 a - 4132138669907\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-170786187a^{2}-463442778a-183958307\right){x}-3836261696323a^{2}-10410020898065a-4132138669907$ |
| 8.1-a4 |
8.1-a |
$4$ |
$4$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{21} \) |
$5.50991$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.731133283$ |
$34.72439287$ |
2.068070635 |
\( \frac{164025}{128} a^{2} - \frac{1086939}{256} a - \frac{108837}{64} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 5\) , \( a^{2} - 2 a - 6\) , \( 479847859799751118 a^{2} + 1302107792384275804 a + 516856787703317587\) , \( -1745931982825887435914314225 a^{2} - 4737734249266514616445813101 a - 1880589394664504575036379429\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(479847859799751118a^{2}+1302107792384275804a+516856787703317587\right){x}-1745931982825887435914314225a^{2}-4737734249266514616445813101a-1880589394664504575036379429$ |
| 8.1-b1 |
8.1-b |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{26} \) |
$5.50991$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{4} \cdot 5 \) |
$0.014744635$ |
$44.54792304$ |
3.615611005 |
\( \frac{98837}{1024} a^{2} - \frac{134541}{1024} a - \frac{808605}{1024} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 5 a^{2} + 13 a + 5\) , \( 116 a^{2} + 315 a + 125\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a^{2}+13a+5\right){x}+116a^{2}+315a+125$ |
| 8.1-c1 |
8.1-c |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
8.1 |
\( 2^{3} \) |
\( - 2^{6} \) |
$5.50991$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.016777694$ |
$378.8407191$ |
1.749359754 |
\( \frac{477495}{4} a^{2} - \frac{353565}{2} a - \frac{3959577}{4} \) |
\( \bigl[1\) , \( -1\) , \( a\) , \( -a - 1\) , \( a + 1\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-1\right){x}+a+1$ |
| 8.2-a1 |
8.2-a |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
8.2 |
\( 2^{3} \) |
\( - 2^{10} \) |
$5.50991$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.556947730$ |
$43.65479198$ |
3.345850667 |
\( -37161 a^{2} + 120317 a + 66352 \) |
\( \bigl[a^{2} - a - 6\) , \( a - 1\) , \( a^{2} - 2 a - 6\) , \( -1472 a^{2} + 4760 a + 2639\) , \( -68891 a^{2} + 222571 a + 123533\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1472a^{2}+4760a+2639\right){x}-68891a^{2}+222571a+123533$ |
| 9.1-a1 |
9.1-a |
$4$ |
$4$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{4} \) |
$5.61914$ |
$(-a^2+2a+7)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.691481895$ |
$226.7404974$ |
3.298653193 |
\( \frac{36545}{9} a^{2} - \frac{73250}{9} a - \frac{27247}{9} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a\) , \( 1\) , \( -40 a^{2} + 130 a + 74\) , \( -341 a^{2} + 1103 a + 609\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-40a^{2}+130a+74\right){x}-341a^{2}+1103a+609$ |
| 9.1-a2 |
9.1-a |
$4$ |
$4$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$5.61914$ |
$(-a^2+2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$3.382963790$ |
$56.68512436$ |
3.298653193 |
\( \frac{403243006}{3} a^{2} - 319160319 a - \frac{554235631}{3} \) |
\( \bigl[a^{2} - 2 a - 5\) , \( a\) , \( 1\) , \( -630 a^{2} + 2045 a + 1099\) , \( -20405 a^{2} + 65957 a + 36465\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-630a^{2}+2045a+1099\right){x}-20405a^{2}+65957a+36465$ |
| 9.1-a3 |
9.1-a |
$4$ |
$4$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{8} \) |
$5.61914$ |
$(-a^2+2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.845740947$ |
$113.3702487$ |
3.298653193 |
\( -\frac{1368562}{81} a^{2} + \frac{2077175}{81} a + \frac{3814639}{27} \) |
\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 3210 a^{2} - 10369 a - 5760\) , \( -6675210 a^{2} + 21565770 a + 11969579\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(3210a^{2}-10369a-5760\right){x}-6675210a^{2}+21565770a+11969579$ |
| 9.1-a4 |
9.1-a |
$4$ |
$4$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{2} \) |
$5.61914$ |
$(-a^2+2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.845740947$ |
$226.7404974$ |
3.298653193 |
\( \frac{140}{3} a^{2} - 531 a + \frac{4039}{3} \) |
\( \bigl[a + 1\) , \( -a^{2} + 3 a + 7\) , \( a^{2} - 2 a - 6\) , \( 4 a + 17\) , \( 7 a + 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-2a-6\right){y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(4a+17\right){x}+7a+10$ |
| 12.2-a1 |
12.2-a |
$2$ |
$2$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{8} \cdot 3^{6} \) |
$5.89513$ |
$(a+2), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.216379105$ |
$54.06511975$ |
3.622223139 |
\( \frac{6539046566}{729} a^{2} + \frac{17673041849}{729} a + \frac{7009010596}{729} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( a^{2} - a - 7\) , \( a\) , \( -15 a^{2} - 45 a - 19\) , \( -138 a^{2} - 374 a - 148\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-15a^{2}-45a-19\right){x}-138a^{2}-374a-148$ |
| 12.2-a2 |
12.2-a |
$2$ |
$2$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
12.2 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{3} \) |
$5.89513$ |
$(a+2), (a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3^{2} \) |
$0.108189552$ |
$216.2604790$ |
3.622223139 |
\( -\frac{59929}{27} a^{2} + \frac{160328}{27} a + \frac{655024}{27} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( a^{2} - a - 7\) , \( a\) , \( -5 a - 4\) , \( -3 a^{2} - 8 a - 3\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-5a-4\right){x}-3a^{2}-8a-3$ |
| 13.1-a1 |
13.1-a |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$5.97430$ |
$(a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.146550917$ |
$150.1354177$ |
1.513916403 |
\( \frac{16384}{13} a^{2} - \frac{12288}{13} a - \frac{110592}{13} \) |
\( \bigl[0\) , \( a^{2} - a - 7\) , \( a^{2} - 2 a - 5\) , \( -75 a^{2} - 196 a - 64\) , \( 920 a^{2} + 2492 a + 976\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-75a^{2}-196a-64\right){x}+920a^{2}+2492a+976$ |
| 13.1-b1 |
13.1-b |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$5.97430$ |
$(a+3)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.024407633$ |
$248.9489915$ |
1.254259785 |
\( \frac{547053568}{13} a^{2} - \frac{526610432}{13} a - \frac{5588054016}{13} \) |
\( \bigl[0\) , \( a^{2} - a - 5\) , \( a^{2} - 2 a - 5\) , \( -5 a^{2} - 28 a - 36\) , \( -77 a^{2} - 150 a + 44\bigr] \) |
${y}^2+\left(a^{2}-2a-5\right){y}={x}^{3}+\left(a^{2}-a-5\right){x}^{2}+\left(-5a^{2}-28a-36\right){x}-77a^{2}-150a+44$ |
| 13.2-a1 |
13.2-a |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
13.2 |
\( 13 \) |
\( 13^{9} \) |
$5.97430$ |
$(a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 3^{2} \) |
$1$ |
$4.828935985$ |
0.996788225 |
\( \frac{1558738593036451}{10604499373} a^{2} - \frac{3005067430377152}{10604499373} a - \frac{10336991206926512}{10604499373} \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( 1312 a^{2} - 1947 a - 10873\) , \( 51570 a^{2} - 76473 a - 427210\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(1312a^{2}-1947a-10873\right){x}+51570a^{2}-76473a-427210$ |
| 13.2-a2 |
13.2-a |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
13.2 |
\( 13 \) |
\( 13^{3} \) |
$5.97430$ |
$(a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$130.3812715$ |
0.996788225 |
\( \frac{2212918}{2197} a^{2} - \frac{7218173}{2197} a - \frac{3620804}{2197} \) |
\( \bigl[a\) , \( -a^{2} + a + 5\) , \( a + 1\) , \( -23 a^{2} + 33 a + 187\) , \( 284 a^{2} - 422 a - 2355\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+5\right){x}^{2}+\left(-23a^{2}+33a+187\right){x}+284a^{2}-422a-2355$ |
| 13.2-b1 |
13.2-b |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
13.2 |
\( 13 \) |
\( -13 \) |
$5.97430$ |
$(a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$2.729455746$ |
$46.10212234$ |
8.658191206 |
\( \frac{33341400251}{13} a^{2} - \frac{49440507617}{13} a - \frac{276200106724}{13} \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{2} + 2 a + 5\) , \( 1\) , \( -6 a^{2} + 7 a + 46\) , \( -3 a^{2} + 14 a + 53\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2a+5\right){x}^{2}+\left(-6a^{2}+7a+46\right){x}-3a^{2}+14a+53$ |
| 13.3-a1 |
13.3-a |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
13.3 |
\( 13 \) |
\( 13 \) |
$5.97430$ |
$(a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$101.5710337$ |
2.329586356 |
\( -\frac{7601}{13} a^{2} + 873 a + \frac{62676}{13} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 6\) , \( a + 1\) , \( -a - 2\) , \( -a - 3\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(-a-2\right){x}-a-3$ |
| 16.1-a1 |
16.1-a |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$6.18467$ |
$(a+2), (-a^2+3a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$173.3722545$ |
3.976386020 |
\( \frac{1297}{8} a^{2} - 731 a + 530 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 7\) , \( a^{2} - a - 6\) , \( -a^{2} + 10\) , \( 2 a^{2} - 3 a - 16\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-2a-7\right){x}^{2}+\left(-a^{2}+10\right){x}+2a^{2}-3a-16$ |
| 16.1-b1 |
16.1-b |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{20} \) |
$6.18467$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.131607088$ |
$34.68296751$ |
5.653250516 |
\( -\frac{72853}{64} a^{2} + \frac{22257}{64} a + \frac{15921}{16} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( a\) , \( a^{2} - a - 6\) , \( -491 a^{2} + 1588 a + 878\) , \( 15394 a^{2} - 49734 a - 27605\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+a{x}^{2}+\left(-491a^{2}+1588a+878\right){x}+15394a^{2}-49734a-27605$ |
| 16.1-b2 |
16.1-b |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$6.18467$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.394821264$ |
$104.0489025$ |
5.653250516 |
\( \frac{1287}{4} a^{2} - 454 a - 1028 \) |
\( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( a\) , \( 96 a^{2} - 311 a - 168\) , \( -166 a^{2} + 537 a + 296\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-2a-5\right){x}^{2}+\left(96a^{2}-311a-168\right){x}-166a^{2}+537a+296$ |
| 16.1-c1 |
16.1-c |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$6.18467$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3^{2} \) |
$0.034679774$ |
$220.3817895$ |
4.732871117 |
\( \frac{1977561833}{8} a^{2} - 798619971 a - 443255358 \) |
\( \bigl[a^{2} - a - 6\) , \( -a^{2} + 3 a + 7\) , \( a^{2} - a - 6\) , \( -5 a^{2} + 3 a + 37\) , \( -4 a^{2} + 32 a + 88\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+3a+7\right){x}^{2}+\left(-5a^{2}+3a+37\right){x}-4a^{2}+32a+88$ |
| 16.1-d1 |
16.1-d |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{6} \) |
$6.18467$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$0.944072279$ |
$196.7885427$ |
4.261024162 |
\( \frac{29097}{2} a^{2} - 46548 a - 27800 \) |
\( \bigl[a^{2} - a - 6\) , \( 0\) , \( 0\) , \( -4 a^{2} + 10 a + 22\) , \( -5 a^{2} + 15 a + 21\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}={x}^{3}+\left(-4a^{2}+10a+22\right){x}-5a^{2}+15a+21$ |
| 16.1-d2 |
16.1-d |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$6.18467$ |
$(a+2), (-a^2+3a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$2.832216837$ |
$7.288464545$ |
4.261024162 |
\( \frac{2480255655721557}{8} a^{2} - \frac{8013025003711473}{8} a - \frac{1111860576650545}{2} \) |
\( \bigl[a^{2} - a - 6\) , \( 0\) , \( 0\) , \( -159 a^{2} + 515 a + 302\) , \( -2484 a^{2} + 7980 a + 4445\bigr] \) |
${y}^2+\left(a^{2}-a-6\right){x}{y}={x}^{3}+\left(-159a^{2}+515a+302\right){x}-2484a^{2}+7980a+4445$ |
| 16.1-e1 |
16.1-e |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$6.18467$ |
$(a+2), (-a^2+3a+3)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
|
\( 2 \cdot 3 \) |
$1$ |
$14.53766694$ |
2.692313415 |
\( -\frac{11242232158325}{2} a^{2} - \frac{61013491788529}{4} a - 6054651719077 \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a^{2} + 3 a + 5\) , \( a^{2} - a - 6\) , \( -15457065941 a^{2} - 41944057048 a - 16649213449\) , \( 3694270556229366 a^{2} + 10024715918186016 a + 3979196267326275\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+3a+5\right){x}^{2}+\left(-15457065941a^{2}-41944057048a-16649213449\right){x}+3694270556229366a^{2}+10024715918186016a+3979196267326275$ |
| 16.1-e2 |
16.1-e |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{20} \) |
$6.18467$ |
$(a+2), (-a^2+3a+3)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
|
\( 2 \cdot 3 \) |
$1$ |
$0.538432108$ |
2.692313415 |
\( -\frac{95863425374298232453}{64} a^{2} + \frac{309708405544939831025}{64} a + \frac{42974103560518372337}{16} \) |
\( \bigl[a\) , \( a + 1\) , \( a^{2} - a - 6\) , \( -1130 a^{2} + 618 a + 560\) , \( 2018 a^{2} + 119374 a + 57163\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1130a^{2}+618a+560\right){x}+2018a^{2}+119374a+57163$ |
| 16.3-a1 |
16.3-a |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{18} \) |
$6.18467$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$1$ |
$46.62881345$ |
2.138913893 |
\( -\frac{122119}{64} a^{2} + \frac{244019}{64} a + \frac{256163}{64} \) |
\( \bigl[a^{2} - 2 a - 6\) , \( a^{2} - a - 7\) , \( a^{2} - a - 6\) , \( -692417 a^{2} - 1878940 a - 745837\) , \( -1220092128 a^{2} - 3310823289 a - 1314193425\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-a-7\right){x}^{2}+\left(-692417a^{2}-1878940a-745837\right){x}-1220092128a^{2}-3310823289a-1314193425$ |
| 16.3-a2 |
16.3-a |
$2$ |
$3$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{30} \) |
$6.18467$ |
$(a+2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$9$ |
\( 2 \) |
$1$ |
$5.180979273$ |
2.138913893 |
\( -\frac{7345147908288439}{262144} a^{2} - \frac{19931682374081821}{262144} a - \frac{7911655846417069}{262144} \) |
\( \bigl[a\) , \( -a^{2} + 2 a + 6\) , \( a^{2} - a - 6\) , \( 1543 a^{2} - 4999 a - 2767\) , \( 4061 a^{2} - 13162 a - 7305\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+2a+6\right){x}^{2}+\left(1543a^{2}-4999a-2767\right){x}+4061a^{2}-13162a-7305$ |
| 16.3-b1 |
16.3-b |
$1$ |
$1$ |
3.3.1901.1 |
$3$ |
$[3, 0]$ |
16.3 |
\( 2^{4} \) |
\( - 2^{10} \) |
$6.18467$ |
$(a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$2.409277990$ |
$19.93706285$ |
6.610103856 |
\( -37161 a^{2} + 120317 a + 66352 \) |
\( \bigl[a^{2} - 2 a - 6\) , \( -a + 1\) , \( 0\) , \( -a^{2} + 17\) , \( -a^{2} + 12\bigr] \) |
${y}^2+\left(a^{2}-2a-6\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a^{2}+17\right){x}-a^{2}+12$ |
*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.
