| Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 28224.a1 |
28224ez1 |
28224.a |
28224ez |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 3^{7} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.401414981$ |
$1$ |
|
$4$ |
$53760$ |
$0.972393$ |
$3584/3$ |
$0.82184$ |
$3.36674$ |
$[0, 0, 0, 2058, -24010]$ |
\(y^2=x^3+2058x-24010\) |
6.2.0.a.1 |
$[(49, 441)]$ |
| 28224.b1 |
28224cv2 |
28224.b |
28224cv |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{14} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.204 |
2B |
$56$ |
$96$ |
$1$ |
$1.577719197$ |
$1$ |
|
$7$ |
$196608$ |
$1.698507$ |
$838561807/26244$ |
$1.03462$ |
$4.43536$ |
$[0, 0, 0, -79212, -8345680]$ |
\(y^2=x^3-79212x-8345680\) |
2.3.0.a.1, 4.12.0.f.1, 8.48.0.q.2, 28.24.0.i.1, 56.96.1.cq.1 |
$[(-154, 448)]$ |
| 28224.b2 |
28224cv1 |
28224.b |
28224cv |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{22} \cdot 3^{10} \cdot 7^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.203 |
2B |
$56$ |
$96$ |
$1$ |
$3.155438394$ |
$1$ |
|
$5$ |
$98304$ |
$1.351934$ |
$4913/1296$ |
$1.13279$ |
$3.85694$ |
$[0, 0, 0, 1428, -442960]$ |
\(y^2=x^3+1428x-442960\) |
2.3.0.a.1, 4.12.0.f.1, 8.48.0.q.1, 14.6.0.b.1, 28.24.0.g.1, $\ldots$ |
$[(133, 1449)]$ |
| 28224.c1 |
28224gp2 |
28224.c |
28224gp |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{7} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$0.665766032$ |
$1$ |
|
$27$ |
$147456$ |
$1.544847$ |
$20720464/63$ |
$0.91015$ |
$4.37336$ |
$[0, 0, 0, -64092, 6228880]$ |
\(y^2=x^3-64092x+6228880\) |
2.3.0.a.1, 12.6.0.c.1, 28.6.0.a.1, 84.12.0.? |
$[(126, 392), (77, 1323)]$ |
| 28224.c2 |
28224gp1 |
28224.c |
28224gp |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{10} \cdot 3^{7} \cdot 7^{8} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$2.663064129$ |
$1$ |
|
$15$ |
$73728$ |
$1.198275$ |
$-16384/147$ |
$1.05520$ |
$3.67940$ |
$[0, 0, 0, -2352, 178360]$ |
\(y^2=x^3-2352x+178360\) |
2.3.0.a.1, 6.6.0.a.1, 28.6.0.b.1, 84.12.0.? |
$[(-7, 441), (42, 392)]$ |
| 28224.d1 |
28224ei1 |
28224.d |
28224ei |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{3} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$2.289693244$ |
$1$ |
|
$3$ |
$12288$ |
$0.283649$ |
$1728$ |
|
$2.59417$ |
$[0, 0, 0, -147, 0]$ |
\(y^2=x^3-147x\) |
|
$[(-12, 6)]$ |
| 28224.d2 |
28224ei2 |
28224.d |
28224ei |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{12} \cdot 3^{3} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1.144846622$ |
$1$ |
|
$7$ |
$24576$ |
$0.630222$ |
$1728$ |
|
$3.00000$ |
$[0, 0, 0, 588, 0]$ |
\(y^2=x^3+588x\) |
|
$[(21, 147)]$ |
| 28224.e1 |
28224go1 |
28224.e |
28224go |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{6} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$1$ |
$57344$ |
$1.044779$ |
$1728$ |
|
$3.48543$ |
$[0, 0, 0, -3087, 0]$ |
\(y^2=x^3-3087x\) |
|
$[ ]$ |
| 28224.e2 |
28224go2 |
28224.e |
28224go |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{12} \cdot 3^{6} \cdot 7^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q(\sqrt{-1})$ |
$-4$ |
$N(\mathrm{U}(1))$ |
|
✓ |
|
|
|
|
|
|
$1$ |
$1$ |
|
$1$ |
$114688$ |
$1.391354$ |
$1728$ |
|
$3.89126$ |
$[0, 0, 0, 12348, 0]$ |
\(y^2=x^3+12348x\) |
|
$[ ]$ |
| 28224.f1 |
28224eh1 |
28224.f |
28224eh |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{14} \cdot 3^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$12$ |
$8$ |
$0$ |
$1.229612500$ |
$1$ |
|
$2$ |
$46080$ |
$0.957685$ |
$-5225472$ |
$1.03482$ |
$3.80104$ |
$[0, 0, 0, -9072, 332640]$ |
\(y^2=x^3-9072x+332640\) |
4.4.0.a.1, 6.2.0.a.1, 12.8.0.c.1 |
$[(57, 27)]$ |
| 28224.g1 |
28224u1 |
28224.g |
28224u |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{14} \cdot 3^{9} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$12$ |
$8$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$46080$ |
$0.957685$ |
$-5225472$ |
$1.03482$ |
$3.80104$ |
$[0, 0, 0, -9072, -332640]$ |
\(y^2=x^3-9072x-332640\) |
4.4.0.a.1, 6.2.0.a.1, 12.8.0.c.1 |
$[ ]$ |
| 28224.h1 |
28224h1 |
28224.h |
28224h |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{14} \cdot 3^{3} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$12$ |
$8$ |
$0$ |
$3.724450301$ |
$1$ |
|
$2$ |
$107520$ |
$1.381334$ |
$-5225472$ |
$1.03482$ |
$4.29712$ |
$[0, 0, 0, -49392, -4225760]$ |
\(y^2=x^3-49392x-4225760\) |
4.4.0.a.1, 6.2.0.a.1, 12.8.0.c.1 |
$[(833, 23079)]$ |
| 28224.i1 |
28224dh1 |
28224.i |
28224dh |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{14} \cdot 3^{3} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.1 |
|
$12$ |
$8$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$107520$ |
$1.381334$ |
$-5225472$ |
$1.03482$ |
$4.29712$ |
$[0, 0, 0, -49392, 4225760]$ |
\(y^2=x^3-49392x+4225760\) |
4.4.0.a.1, 6.2.0.a.1, 12.8.0.c.1 |
$[ ]$ |
| 28224.j1 |
28224cu2 |
28224.j |
28224cu |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$2.508907243$ |
$1$ |
|
$5$ |
$147456$ |
$1.544847$ |
$20720464/63$ |
$0.91015$ |
$4.37336$ |
$[0, 0, 0, -64092, -6228880]$ |
\(y^2=x^3-64092x-6228880\) |
2.3.0.a.1, 12.6.0.c.1, 28.6.0.a.1, 84.12.0.? |
$[(-152, 36)]$ |
| 28224.j2 |
28224cu1 |
28224.j |
28224cu |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{10} \cdot 3^{7} \cdot 7^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1.254453621$ |
$1$ |
|
$7$ |
$73728$ |
$1.198275$ |
$-16384/147$ |
$1.05520$ |
$3.67940$ |
$[0, 0, 0, -2352, -178360]$ |
\(y^2=x^3-2352x-178360\) |
2.3.0.a.1, 6.6.0.a.1, 28.6.0.b.1, 84.12.0.? |
$[(154, 1764)]$ |
| 28224.k1 |
28224gq2 |
28224.k |
28224gq |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{20} \cdot 3^{14} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.204 |
2B |
$56$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$196608$ |
$1.698507$ |
$838561807/26244$ |
$1.03462$ |
$4.43536$ |
$[0, 0, 0, -79212, 8345680]$ |
\(y^2=x^3-79212x+8345680\) |
2.3.0.a.1, 4.12.0.f.1, 8.48.0.q.2, 28.24.0.i.1, 56.96.1.cq.1 |
$[ ]$ |
| 28224.k2 |
28224gq1 |
28224.k |
28224gq |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{22} \cdot 3^{10} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.203 |
2B |
$56$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$98304$ |
$1.351934$ |
$4913/1296$ |
$1.13279$ |
$3.85694$ |
$[0, 0, 0, 1428, 442960]$ |
\(y^2=x^3+1428x+442960\) |
2.3.0.a.1, 4.12.0.f.1, 8.48.0.q.1, 14.6.0.b.1, 28.24.0.g.1, $\ldots$ |
$[ ]$ |
| 28224.l1 |
28224ey1 |
28224.l |
28224ey |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{6} \cdot 3^{7} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$3.362589813$ |
$1$ |
|
$2$ |
$53760$ |
$0.972393$ |
$3584/3$ |
$0.82184$ |
$3.36674$ |
$[0, 0, 0, 2058, 24010]$ |
\(y^2=x^3+2058x+24010\) |
6.2.0.a.1 |
$[(53, 531)]$ |
| 28224.m1 |
28224df1 |
28224.m |
28224df |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{15} \cdot 3^{3} \cdot 7^{8} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$24$ |
$2$ |
$0$ |
$0.592445688$ |
$1$ |
|
$18$ |
$53760$ |
$1.127153$ |
$1512$ |
$0.78795$ |
$3.56965$ |
$[0, 0, 0, 4116, 38416]$ |
\(y^2=x^3+4116x+38416\) |
24.2.0.b.1 |
$[(98, 1176), (245, 3969)]$ |
| 28224.n1 |
28224ee1 |
28224.n |
28224ee |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{15} \cdot 3^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$24$ |
$2$ |
$0$ |
$0.663025789$ |
$1$ |
|
$4$ |
$23040$ |
$0.703504$ |
$1512$ |
$0.78795$ |
$3.07357$ |
$[0, 0, 0, 756, -3024]$ |
\(y^2=x^3+756x-3024\) |
24.2.0.b.1 |
$[(30, 216)]$ |
| 28224.o1 |
28224gi2 |
28224.o |
28224gi |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{33} \cdot 3^{7} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$168$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1935360$ |
$3.008900$ |
$-16591834777/98304$ |
$1.06741$ |
$6.05681$ |
$[0, 0, 0, -20081964, 34815229904]$ |
\(y^2=x^3-20081964x+34815229904\) |
3.4.0.a.1, 24.8.0.d.1, 84.8.0.?, 168.16.0.? |
$[ ]$ |
| 28224.o2 |
28224gi1 |
28224.o |
28224gi |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{23} \cdot 3^{9} \cdot 7^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$168$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$645120$ |
$2.459595$ |
$596183/864$ |
$1.03569$ |
$5.09703$ |
$[0, 0, 0, 662676, 254659664]$ |
\(y^2=x^3+662676x+254659664\) |
3.4.0.a.1, 24.8.0.d.1, 84.8.0.?, 168.16.0.? |
$[ ]$ |
| 28224.p1 |
28224dd2 |
28224.p |
28224dd |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{21} \cdot 3^{9} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.2 |
3B |
$504$ |
$144$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$580608$ |
$2.359760$ |
$-67645179/8$ |
$1.03261$ |
$5.46076$ |
$[0, 0, 0, -2630124, 1641938256]$ |
\(y^2=x^3-2630124x+1641938256\) |
3.4.0.a.1, 9.12.0.b.1, 12.8.0-3.a.1.3, 24.16.0-24.d.1.5, 36.24.0-9.b.1.4, $\ldots$ |
$[ ]$ |
| 28224.p2 |
28224dd1 |
28224.p |
28224dd |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{27} \cdot 3^{3} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.2 |
3B |
$504$ |
$144$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$193536$ |
$1.810455$ |
$189/512$ |
$1.32659$ |
$4.39431$ |
$[0, 0, 0, 4116, 6953296]$ |
\(y^2=x^3+4116x+6953296\) |
3.4.0.a.1, 9.12.0.b.1, 12.8.0-3.a.1.4, 24.16.0-24.d.1.6, 36.24.0-9.b.1.3, $\ldots$ |
$[ ]$ |
| 28224.q1 |
28224cp2 |
28224.q |
28224cp |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.12.0.2 |
2Cn, 3B |
$504$ |
$864$ |
$28$ |
$6.917102010$ |
$1$ |
|
$0$ |
$17280$ |
$0.690845$ |
$406749952$ |
$0.99897$ |
$3.63378$ |
$[0, 0, 0, -5124, -141176]$ |
\(y^2=x^3-5124x-141176\) |
2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 9.12.0.b.1, 12.16.0.a.1, $\ldots$ |
$[(-11955/17, 1651/17)]$ |
| 28224.q2 |
28224cp1 |
28224.q |
28224cp |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.12.0.2 |
2Cn, 3B |
$504$ |
$864$ |
$28$ |
$2.305700670$ |
$1$ |
|
$2$ |
$5760$ |
$0.141539$ |
$1792$ |
$0.89152$ |
$2.43035$ |
$[0, 0, 0, -84, -56]$ |
\(y^2=x^3-84x-56\) |
2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 9.12.0.b.1, 12.16.0.a.2, $\ldots$ |
$[(-3, 13)]$ |
| 28224.r1 |
28224s1 |
28224.r |
28224s |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{21} \cdot 3^{3} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.2 |
3B |
$504$ |
$144$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$27648$ |
$0.837500$ |
$-67645179/8$ |
$1.03261$ |
$3.67824$ |
$[0, 0, 0, -5964, -177296]$ |
\(y^2=x^3-5964x-177296\) |
3.4.0.a.1, 9.12.0.b.1, 24.8.0.d.1, 42.8.0-3.a.1.1, 63.36.0.i.2, $\ldots$ |
$[ ]$ |
| 28224.r2 |
28224s2 |
28224.r |
28224s |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{27} \cdot 3^{9} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.2 |
3B |
$504$ |
$144$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$82944$ |
$1.386806$ |
$189/512$ |
$1.32659$ |
$3.89823$ |
$[0, 0, 0, 756, -547344]$ |
\(y^2=x^3+756x-547344\) |
3.4.0.a.1, 9.12.0.b.1, 24.8.0.d.1, 42.8.0-3.a.1.2, 63.36.0.i.1, $\ldots$ |
$[ ]$ |
| 28224.s1 |
28224gg1 |
28224.s |
28224gg |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{15} \cdot 3^{9} \cdot 7^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$24$ |
$2$ |
$0$ |
$0.375270760$ |
$1$ |
|
$16$ |
$27648$ |
$0.815107$ |
$-1668296/27$ |
$0.92232$ |
$3.43831$ |
$[0, 0, 0, -2604, 51856]$ |
\(y^2=x^3-2604x+51856\) |
24.2.0.b.1 |
$[(2, 216), (50, 216)]$ |
| 28224.t1 |
28224gf1 |
28224.t |
28224gf |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{15} \cdot 3^{9} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$27648$ |
$0.815107$ |
$-1668296/27$ |
$0.92232$ |
$3.43831$ |
$[0, 0, 0, -2604, -51856]$ |
\(y^2=x^3-2604x-51856\) |
24.2.0.b.1 |
$[ ]$ |
| 28224.u1 |
28224co2 |
28224.u |
28224co |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{33} \cdot 3^{7} \cdot 7^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$168$ |
$16$ |
$0$ |
$13.99083305$ |
$1$ |
|
$0$ |
$1935360$ |
$3.008900$ |
$-16591834777/98304$ |
$1.06741$ |
$6.05681$ |
$[0, 0, 0, -20081964, -34815229904]$ |
\(y^2=x^3-20081964x-34815229904\) |
3.4.0.a.1, 24.8.0.d.1, 42.8.0-3.a.1.1, 168.16.0.? |
$[(9096308/11, 27384630624/11)]$ |
| 28224.u2 |
28224co1 |
28224.u |
28224co |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{23} \cdot 3^{9} \cdot 7^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$168$ |
$16$ |
$0$ |
$4.663611018$ |
$1$ |
|
$2$ |
$645120$ |
$2.459595$ |
$596183/864$ |
$1.03569$ |
$5.09703$ |
$[0, 0, 0, 662676, -254659664]$ |
\(y^2=x^3+662676x-254659664\) |
3.4.0.a.1, 24.8.0.d.1, 42.8.0-3.a.1.2, 168.16.0.? |
$[(884, 31968)]$ |
| 28224.v1 |
28224f2 |
28224.v |
28224f |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{21} \cdot 3^{9} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.2 |
3B |
$504$ |
$144$ |
$2$ |
$5.939986572$ |
$1$ |
|
$2$ |
$580608$ |
$2.359760$ |
$-67645179/8$ |
$1.03261$ |
$5.46076$ |
$[0, 0, 0, -2630124, -1641938256]$ |
\(y^2=x^3-2630124x-1641938256\) |
3.4.0.a.1, 6.8.0-3.a.1.1, 9.12.0.b.1, 18.24.0-9.b.1.1, 24.16.0-24.d.1.2, $\ldots$ |
$[(3012, 133272)]$ |
| 28224.v2 |
28224f1 |
28224.v |
28224f |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{27} \cdot 3^{3} \cdot 7^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.2 |
3B |
$504$ |
$144$ |
$2$ |
$1.979995524$ |
$1$ |
|
$2$ |
$193536$ |
$1.810455$ |
$189/512$ |
$1.32659$ |
$4.39431$ |
$[0, 0, 0, 4116, -6953296]$ |
\(y^2=x^3+4116x-6953296\) |
3.4.0.a.1, 6.8.0-3.a.1.2, 9.12.0.b.1, 18.24.0-9.b.1.2, 24.16.0-24.d.1.1, $\ldots$ |
$[(196, 1176)]$ |
| 28224.w1 |
28224gh2 |
28224.w |
28224gh |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.12.0.2 |
2Cn, 3B |
$504$ |
$864$ |
$28$ |
$1$ |
$1$ |
|
$0$ |
$17280$ |
$0.690845$ |
$406749952$ |
$0.99897$ |
$3.63378$ |
$[0, 0, 0, -5124, 141176]$ |
\(y^2=x^3-5124x+141176\) |
2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 9.12.0.b.1, 12.16.0.a.1, $\ldots$ |
$[ ]$ |
| 28224.w2 |
28224gh1 |
28224.w |
28224gh |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 3$ |
2.2.0.1, 9.12.0.2 |
2Cn, 3B |
$504$ |
$864$ |
$28$ |
$1$ |
$1$ |
|
$0$ |
$5760$ |
$0.141539$ |
$1792$ |
$0.89152$ |
$2.43035$ |
$[0, 0, 0, -84, 56]$ |
\(y^2=x^3-84x+56\) |
2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 9.12.0.b.1, 12.16.0.a.2, $\ldots$ |
$[ ]$ |
| 28224.x1 |
28224ec1 |
28224.x |
28224ec |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{21} \cdot 3^{3} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.2 |
3B |
$504$ |
$144$ |
$2$ |
$0.424331189$ |
$1$ |
|
$4$ |
$27648$ |
$0.837500$ |
$-67645179/8$ |
$1.03261$ |
$3.67824$ |
$[0, 0, 0, -5964, 177296]$ |
\(y^2=x^3-5964x+177296\) |
3.4.0.a.1, 9.12.0.b.1, 24.8.0.d.1, 63.36.0.i.2, 72.24.0.?, $\ldots$ |
$[(50, 64)]$ |
| 28224.x2 |
28224ec2 |
28224.x |
28224ec |
$2$ |
$3$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{27} \cdot 3^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.12.0.2 |
3B |
$504$ |
$144$ |
$2$ |
$1.272993569$ |
$1$ |
|
$4$ |
$82944$ |
$1.386806$ |
$189/512$ |
$1.32659$ |
$3.89823$ |
$[0, 0, 0, 756, 547344]$ |
\(y^2=x^3+756x+547344\) |
3.4.0.a.1, 9.12.0.b.1, 24.8.0.d.1, 63.36.0.i.1, 72.24.0.?, $\ldots$ |
$[(-62, 512)]$ |
| 28224.y1 |
28224de1 |
28224.y |
28224de |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{15} \cdot 3^{3} \cdot 7^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$53760$ |
$1.127153$ |
$1512$ |
$0.78795$ |
$3.56965$ |
$[0, 0, 0, 4116, -38416]$ |
\(y^2=x^3+4116x-38416\) |
24.2.0.b.1 |
$[ ]$ |
| 28224.z1 |
28224ed1 |
28224.z |
28224ed |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{15} \cdot 3^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$24$ |
$2$ |
$0$ |
$1.706553261$ |
$1$ |
|
$2$ |
$23040$ |
$0.703504$ |
$1512$ |
$0.78795$ |
$3.07357$ |
$[0, 0, 0, 756, 3024]$ |
\(y^2=x^3+756x+3024\) |
24.2.0.b.1 |
$[(-3, 27)]$ |
| 28224.ba1 |
28224dy1 |
28224.ba |
28224dy |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{10} \cdot 3^{3} \cdot 7^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$0.693636348$ |
$1$ |
|
$7$ |
$24576$ |
$0.716607$ |
$55296/7$ |
$0.81576$ |
$3.20291$ |
$[0, 0, 0, -1176, 13720]$ |
\(y^2=x^3-1176x+13720\) |
2.3.0.a.1, 12.6.0.c.1, 28.6.0.d.1, 42.6.0.a.1, 84.12.0.? |
$[(42, 196)]$ |
| 28224.ba2 |
28224dy2 |
28224.ba |
28224dy |
$2$ |
$2$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{14} \cdot 3^{3} \cdot 7^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$84$ |
$12$ |
$0$ |
$1.387272696$ |
$1$ |
|
$5$ |
$49152$ |
$1.063181$ |
$11664/49$ |
$0.83745$ |
$3.50058$ |
$[0, 0, 0, 1764, 71344]$ |
\(y^2=x^3+1764x+71344\) |
2.3.0.a.1, 6.6.0.a.1, 28.6.0.d.1, 84.12.0.? |
$[(21, 343)]$ |
| 28224.bb1 |
28224cn1 |
28224.bb |
28224cn |
$1$ |
$1$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{14} \cdot 3^{9} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1.735235231$ |
$1$ |
|
$2$ |
$18432$ |
$0.642578$ |
$-7168/27$ |
$0.94787$ |
$3.03291$ |
$[0, 0, 0, -336, -6496]$ |
\(y^2=x^3-336x-6496\) |
6.2.0.a.1 |
$[(25, 27)]$ |
| 28224.bc1 |
28224cl4 |
28224.bc |
28224cl |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{15} \cdot 3^{7} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$168$ |
$48$ |
$0$ |
$3.039688290$ |
$1$ |
|
$5$ |
$73728$ |
$1.442614$ |
$7301384/3$ |
$1.03749$ |
$4.33921$ |
$[0, 0, 0, -57036, -5241040]$ |
\(y^2=x^3-57036x-5241040\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0.bi.1, 56.24.0-8.m.1.7, $\ldots$ |
$[(-136, 20)]$ |
| 28224.bc2 |
28224cl2 |
28224.bc |
28224cl |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.4 |
2Cs |
$168$ |
$48$ |
$0$ |
$1.519844145$ |
$1$ |
|
$11$ |
$36864$ |
$1.096041$ |
$21952/9$ |
$1.09175$ |
$3.56965$ |
$[0, 0, 0, -4116, -54880]$ |
\(y^2=x^3-4116x-54880\) |
2.6.0.a.1, 8.12.0.b.1, 12.12.0.a.1, 24.24.0.f.1, 28.12.0-2.a.1.2, $\ldots$ |
$[(-38, 216)]$ |
| 28224.bc3 |
28224cl1 |
28224.bc |
28224cl |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{6} \cdot 3^{7} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.11 |
2B |
$168$ |
$48$ |
$0$ |
$3.039688290$ |
$1$ |
|
$3$ |
$18432$ |
$0.749467$ |
$140608/3$ |
$1.02705$ |
$3.34504$ |
$[0, 0, 0, -1911, 31556]$ |
\(y^2=x^3-1911x+31556\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0.h.1, 24.24.0.bk.1, $\ldots$ |
$[(64, 414)]$ |
| 28224.bc4 |
28224cl3 |
28224.bc |
28224cl |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( - 2^{15} \cdot 3^{10} \cdot 7^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.16 |
2B |
$168$ |
$48$ |
$0$ |
$3.039688290$ |
$1$ |
|
$5$ |
$73728$ |
$1.442614$ |
$97336/81$ |
$1.05989$ |
$3.91789$ |
$[0, 0, 0, 13524, -400624]$ |
\(y^2=x^3+13524x-400624\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 24.24.0.n.1, 56.24.0-8.d.1.4, $\ldots$ |
$[(109, 1539)]$ |
| 28224.bd1 |
28224ck4 |
28224.bd |
28224ck |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{17} \cdot 3^{6} \cdot 7^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$168$ |
$48$ |
$0$ |
$3.860942544$ |
$1$ |
|
$5$ |
$196608$ |
$1.866802$ |
$1443468546/7$ |
$1.04654$ |
$4.99037$ |
$[0, 0, 0, -527436, 147435120]$ |
\(y^2=x^3-527436x+147435120\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 24.24.0-8.p.1.2, 56.24.0.bp.1, $\ldots$ |
$[(421, 55)]$ |
| 28224.bd2 |
28224ck3 |
28224.bd |
28224ck |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{17} \cdot 3^{6} \cdot 7^{10} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.15 |
2B |
$168$ |
$48$ |
$0$ |
$3.860942544$ |
$1$ |
|
$5$ |
$196608$ |
$1.866802$ |
$11090466/2401$ |
$1.11706$ |
$4.51528$ |
$[0, 0, 0, -104076, -10224144]$ |
\(y^2=x^3-104076x-10224144\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 24.24.0-8.k.1.4, 56.24.0.v.1, $\ldots$ |
$[(-216, 1476)]$ |
| 28224.bd3 |
28224ck2 |
28224.bd |
28224ck |
$4$ |
$4$ |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{6} \cdot 7^{8} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.3 |
2Cs |
$168$ |
$48$ |
$0$ |
$1.930471272$ |
$1$ |
|
$11$ |
$98304$ |
$1.520229$ |
$740772/49$ |
$1.06534$ |
$4.18357$ |
$[0, 0, 0, -33516, 2222640]$ |
\(y^2=x^3-33516x+2222640\) |
2.6.0.a.1, 8.12.0.a.1, 12.12.0-2.a.1.2, 24.24.0-8.a.1.4, 28.12.0.b.1, $\ldots$ |
$[(78, 288)]$ |
