| 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 |
Intrinsic torsion order |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
Manin constant |
| 13872.a1 |
13872h1 |
13872.a |
13872h |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{4} \cdot 3 \cdot 17^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$24480$ |
$0.955894$ |
$-34816/3$ |
$1.03262$ |
$3.77819$ |
$1$ |
$[0, -1, 0, -3275, 78426]$ |
\(y^2=x^3-x^2-3275x+78426\) |
6.2.0.a.1 |
$[ ]$ |
$1$ |
| 13872.b1 |
13872c1 |
13872.b |
13872c |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 17^{11} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$3.886305152$ |
$1$ |
|
$0$ |
$138240$ |
$2.022617$ |
$57530252288/38336139$ |
$1.04113$ |
$4.96141$ |
$1$ |
$[0, -1, 0, 147583, 8444109]$ |
\(y^2=x^3-x^2+147583x+8444109\) |
102.2.0.? |
$[(26812/3, 4426613/3)]$ |
$1$ |
| 13872.c1 |
13872bb2 |
13872.c |
13872bb |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{15} \cdot 3^{3} \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.9 |
3B |
$72$ |
$144$ |
$2$ |
$4.921731266$ |
$1$ |
|
$2$ |
$2776032$ |
$3.312298$ |
$-843137281012581793/216$ |
$1.08401$ |
$7.57624$ |
$1$ |
$[0, -1, 0, -601693472, 5681021020416]$ |
\(y^2=x^3-x^2-601693472x+5681021020416\) |
3.4.0.a.1, 9.36.0.f.1, 12.8.0-3.a.1.2, 24.16.0-24.d.1.4, 36.72.0-9.f.1.1, $\ldots$ |
$[(14464, 62384)]$ |
$1$ |
| 13872.c2 |
13872bb1 |
13872.c |
13872bb |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{21} \cdot 3^{9} \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.36.0.7 |
3B |
$72$ |
$144$ |
$2$ |
$1.640577088$ |
$1$ |
|
$2$ |
$925344$ |
$2.762993$ |
$-1579268174113/10077696$ |
$1.03714$ |
$6.19467$ |
$1$ |
$[0, -1, 0, -7416992, 7820031744]$ |
\(y^2=x^3-x^2-7416992x+7820031744\) |
3.4.0.a.1, 9.36.0.f.2, 12.8.0-3.a.1.1, 24.16.0-24.d.1.3, 36.72.0-9.f.2.1, $\ldots$ |
$[(4528, 258944)]$ |
$1$ |
| 13872.d1 |
13872ba1 |
13872.d |
13872ba |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{4} \cdot 3^{5} \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.5.0.1 |
5S4 |
$30$ |
$10$ |
$0$ |
$8.185346581$ |
$1$ |
|
$0$ |
$36720$ |
$1.265120$ |
$278528/243$ |
$1.03702$ |
$3.98166$ |
$1$ |
$[0, -1, 0, 6551, -147572]$ |
\(y^2=x^3-x^2+6551x-147572\) |
5.5.0.a.1, 6.2.0.a.1, 30.10.0.a.1 |
$[(3208/3, 185786/3)]$ |
$1$ |
| 13872.e1 |
13872v1 |
13872.e |
13872v |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{4} \cdot 3^{7} \cdot 17^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3024$ |
$0.184585$ |
$-370720768/2187$ |
$1.05186$ |
$2.95463$ |
$1$ |
$[0, -1, 0, -249, -1440]$ |
\(y^2=x^3-x^2-249x-1440\) |
6.2.0.a.1 |
$[ ]$ |
$1$ |
| 13872.f1 |
13872w4 |
13872.f |
13872w |
$4$ |
$10$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{13} \cdot 3^{20} \cdot 17^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 5$ |
8.6.0.2, 5.6.0.1 |
2B, 5B |
$680$ |
$288$ |
$5$ |
$1$ |
$4$ |
$2$ |
$1$ |
$2611200$ |
$3.480015$ |
$211293405175481/6973568802$ |
$1.13518$ |
$7.00394$ |
$1$ |
$[0, -1, 0, -97541064, 360095102064]$ |
\(y^2=x^3-x^2-97541064x+360095102064\) |
2.3.0.a.1, 5.6.0.a.1, 8.6.0.f.1, 10.18.0.a.1, 20.36.0.b.2, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.f2 |
13872w3 |
13872.f |
13872w |
$4$ |
$10$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{14} \cdot 3^{10} \cdot 17^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 5$ |
8.6.0.2, 5.6.0.1 |
2B, 5B |
$680$ |
$288$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$1305600$ |
$3.133442$ |
$206226044828441/236196$ |
$1.07449$ |
$7.00139$ |
$1$ |
$[0, -1, 0, -96754984, 366349783408]$ |
\(y^2=x^3-x^2-96754984x+366349783408\) |
2.3.0.a.1, 5.6.0.a.1, 8.6.0.f.1, 10.36.0.b.1, 34.6.0.a.1, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.f3 |
13872w2 |
13872.f |
13872w |
$4$ |
$10$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{17} \cdot 3^{4} \cdot 17^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 5$ |
8.6.0.2, 5.6.0.1 |
2B, 5B |
$680$ |
$288$ |
$5$ |
$1$ |
$4$ |
$2$ |
$1$ |
$522240$ |
$2.675297$ |
$551569744601/2592$ |
$1.20056$ |
$6.38028$ |
$1$ |
$[0, -1, 0, -13430504, -18940096656]$ |
\(y^2=x^3-x^2-13430504x-18940096656\) |
2.3.0.a.1, 5.6.0.a.1, 8.6.0.f.1, 10.18.0.a.1, 20.36.0.b.1, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.f4 |
13872w1 |
13872.f |
13872w |
$4$ |
$10$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{22} \cdot 3^{2} \cdot 17^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 5$ |
8.6.0.2, 5.6.0.1 |
2B, 5B |
$680$ |
$288$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$261120$ |
$2.328720$ |
$141420761/9216$ |
$0.99890$ |
$5.51331$ |
$1$ |
$[0, -1, 0, -853224, -285474960]$ |
\(y^2=x^3-x^2-853224x-285474960\) |
2.3.0.a.1, 5.6.0.a.1, 8.6.0.f.1, 10.36.0.b.2, 34.6.0.a.1, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.g1 |
13872r1 |
13872.g |
13872r |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 17^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.84 |
2B |
$816$ |
$192$ |
$5$ |
$1$ |
$1$ |
|
$1$ |
$104448$ |
$1.890018$ |
$274625/81$ |
$0.94244$ |
$4.85863$ |
$1$ |
$[0, -1, 0, -106448, -9325056]$ |
\(y^2=x^3-x^2-106448x-9325056\) |
2.3.0.a.1, 4.12.0.f.1, 8.24.0.bh.1, 34.6.0.a.1, 48.48.1.gv.1, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.g2 |
13872r2 |
13872.g |
13872r |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{12} \cdot 3^{8} \cdot 17^{9} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.127 |
2B |
$816$ |
$192$ |
$5$ |
$1$ |
$4$ |
$2$ |
$1$ |
$208896$ |
$2.236591$ |
$5359375/6561$ |
$1.11521$ |
$5.18161$ |
$1$ |
$[0, -1, 0, 286592, -62464064]$ |
\(y^2=x^3-x^2+286592x-62464064\) |
2.3.0.a.1, 4.6.0.e.1, 8.24.0.bj.1, 48.48.1.gx.1, 68.12.0.l.1, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.h1 |
13872a1 |
13872.h |
13872a |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{8} \cdot 3^{3} \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1.710913826$ |
$1$ |
|
$2$ |
$1728$ |
$-0.092596$ |
$-34000/27$ |
$0.81216$ |
$2.36008$ |
$1$ |
$[0, -1, 0, -28, -80]$ |
\(y^2=x^3-x^2-28x-80\) |
6.2.0.a.1 |
$[(8, 12)]$ |
$1$ |
| 13872.i1 |
13872d1 |
13872.i |
13872d |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{10} \cdot 3 \cdot 17^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$48960$ |
$1.567677$ |
$-18674500/3$ |
$0.93197$ |
$4.85866$ |
$1$ |
$[0, -1, 0, -106448, -13334064]$ |
\(y^2=x^3-x^2-106448x-13334064\) |
6.2.0.a.1 |
$[ ]$ |
$1$ |
| 13872.j1 |
13872z2 |
13872.j |
13872z |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{30} \cdot 3 \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$36$ |
$48$ |
$0$ |
$5.156334848$ |
$1$ |
|
$0$ |
$264384$ |
$2.441677$ |
$-4999353625/786432$ |
$1.12790$ |
$5.61529$ |
$1$ |
$[0, -1, 0, -1089048, 493687536]$ |
\(y^2=x^3-x^2-1089048x+493687536\) |
3.4.0.a.1, 6.8.0.b.1, 12.16.0-6.b.1.2, 18.24.0.c.1, 36.48.0-18.c.1.1 |
$[(-9428/3, 593920/3)]$ |
$1$ |
| 13872.j2 |
13872z1 |
13872.j |
13872z |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{18} \cdot 3^{3} \cdot 17^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$12$ |
$48$ |
$0$ |
$1.718778282$ |
$1$ |
|
$0$ |
$88128$ |
$1.892372$ |
$2828375/1728$ |
$1.02006$ |
$4.80609$ |
$1$ |
$[0, -1, 0, 90072, -2486160]$ |
\(y^2=x^3-x^2+90072x-2486160\) |
3.4.0.a.1, 6.24.0.c.1, 12.48.0-6.c.1.1 |
$[(292/3, 18496/3)]$ |
$1$ |
| 13872.k1 |
13872e1 |
13872.k |
13872e |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{4} \cdot 3^{11} \cdot 17^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$15840$ |
$0.870678$ |
$-73984000/177147$ |
$1.11146$ |
$3.55029$ |
$1$ |
$[0, -1, 0, -963, 26406]$ |
\(y^2=x^3-x^2-963x+26406\) |
6.2.0.a.1 |
$[ ]$ |
$1$ |
| 13872.l1 |
13872f1 |
13872.l |
13872f |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{11} \cdot 3^{3} \cdot 17^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$12960$ |
$0.818529$ |
$-68001122/27$ |
$1.13780$ |
$3.87866$ |
$1$ |
$[0, -1, 0, -4720, -123296]$ |
\(y^2=x^3-x^2-4720x-123296\) |
24.2.0.b.1 |
$[ ]$ |
$1$ |
| 13872.m1 |
13872s1 |
13872.m |
13872s |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{8} \cdot 3^{7} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5376$ |
$0.490478$ |
$-8192/2187$ |
$1.26266$ |
$3.06072$ |
$1$ |
$[0, -1, 0, -45, -2511]$ |
\(y^2=x^3-x^2-45x-2511\) |
102.2.0.? |
$[ ]$ |
$1$ |
| 13872.n1 |
13872u1 |
13872.n |
13872u |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{19} \cdot 3 \cdot 17^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$6048$ |
$0.340828$ |
$5831/384$ |
$1.01027$ |
$2.87081$ |
$1$ |
$[0, -1, 0, 40, 1008]$ |
\(y^2=x^3-x^2+40x+1008\) |
24.2.0.b.1 |
$[ ]$ |
$1$ |
| 13872.o1 |
13872t1 |
13872.o |
13872t |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{8} \cdot 3^{11} \cdot 17^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$152064$ |
$2.018509$ |
$-1841198792704/3011499$ |
$1.22809$ |
$5.32509$ |
$1$ |
$[0, -1, 0, -468565, 123784009]$ |
\(y^2=x^3-x^2-468565x+123784009\) |
102.2.0.? |
$[ ]$ |
$1$ |
| 13872.p1 |
13872b5 |
13872.p |
13872b |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{2} \cdot 17^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.210 |
2B |
$816$ |
$192$ |
$1$ |
$1.492303742$ |
$1$ |
|
$3$ |
$40960$ |
$1.464401$ |
$3065617154/9$ |
$1.21059$ |
$4.87201$ |
$2$ |
$[0, -1, 0, -111072, 14285088]$ |
\(y^2=x^3-x^2-111072x+14285088\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.r.1, 16.48.0.l.1, 24.48.0.bf.1, $\ldots$ |
$[(261, 1734)]$ |
$1$ |
| 13872.p2 |
13872b3 |
13872.p |
13872b |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{10} \cdot 3 \cdot 17^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.127 |
2B |
$816$ |
$192$ |
$1$ |
$11.93842994$ |
$1$ |
|
$1$ |
$20480$ |
$1.117828$ |
$28756228/3$ |
$1.05617$ |
$4.30978$ |
$2$ |
$[0, -1, 0, -18592, -969488]$ |
\(y^2=x^3-x^2-18592x-969488\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 12.12.0.h.1, 16.48.0.bb.2, $\ldots$ |
$[(-702159/95, 2141464/95)]$ |
$1$ |
| 13872.p3 |
13872b4 |
13872.p |
13872b |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.88 |
2Cs |
$408$ |
$192$ |
$1$ |
$2.984607485$ |
$1$ |
|
$7$ |
$20480$ |
$1.117828$ |
$1556068/81$ |
$1.03212$ |
$4.00398$ |
$1$ |
$[0, -1, 0, -7032, 218880]$ |
\(y^2=x^3-x^2-7032x+218880\) |
2.6.0.a.1, 4.12.0.b.1, 8.48.0.e.2, 24.96.1.bl.2, 68.24.0-4.b.1.3, $\ldots$ |
$[(32, 160)]$ |
$1$ |
| 13872.p4 |
13872b2 |
13872.p |
13872b |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 17^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.138 |
2Cs |
$408$ |
$192$ |
$1$ |
$5.969214971$ |
$1$ |
|
$3$ |
$10240$ |
$0.771255$ |
$35152/9$ |
$0.97255$ |
$3.46123$ |
$1$ |
$[0, -1, 0, -1252, -12320]$ |
\(y^2=x^3-x^2-1252x-12320\) |
2.6.0.a.1, 4.12.0.b.1, 8.48.0.h.1, 12.24.0.c.1, 24.96.1.bu.1, $\ldots$ |
$[(-444/5, 7904/5)]$ |
$1$ |
| 13872.p5 |
13872b1 |
13872.p |
13872b |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{4} \cdot 3 \cdot 17^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.150 |
2B |
$816$ |
$192$ |
$1$ |
$11.93842994$ |
$1$ |
|
$1$ |
$5120$ |
$0.424681$ |
$2048/3$ |
$1.17572$ |
$2.91714$ |
$2$ |
$[0, -1, 0, 193, -1338]$ |
\(y^2=x^3-x^2+193x-1338\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.ba.1, 12.12.0.g.1, $\ldots$ |
$[(117766/65, 43353136/65)]$ |
$1$ |
| 13872.p6 |
13872b6 |
13872.p |
13872b |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{11} \cdot 3^{8} \cdot 17^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.218 |
2B |
$816$ |
$192$ |
$1$ |
$1.492303742$ |
$1$ |
|
$7$ |
$40960$ |
$1.464401$ |
$207646/6561$ |
$1.15980$ |
$4.28293$ |
$2$ |
$[0, -1, 0, 4528, 856992]$ |
\(y^2=x^3-x^2+4528x+856992\) |
2.3.0.a.1, 4.6.0.c.1, 8.48.0.m.1, 48.96.1.w.2, 68.12.0-4.c.1.2, $\ldots$ |
$[(-62, 578)]$ |
$1$ |
| 13872.q1 |
13872x2 |
13872.q |
13872x |
$2$ |
$5$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{12} \cdot 3^{5} \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$1020$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$19200$ |
$0.986022$ |
$-13549359104/243$ |
$1.07715$ |
$4.20933$ |
$1$ |
$[0, -1, 0, -13509, 608877]$ |
\(y^2=x^3-x^2-13509x+608877\) |
5.6.0.a.1, 30.12.0.a.1, 85.12.0.?, 102.2.0.?, 340.24.0.?, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.q2 |
13872x1 |
13872.q |
13872x |
$2$ |
$5$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{12} \cdot 3 \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$1020$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$3840$ |
$0.181303$ |
$4096/3$ |
$0.95016$ |
$2.63537$ |
$1$ |
$[0, -1, 0, 91, 141]$ |
\(y^2=x^3-x^2+91x+141\) |
5.6.0.a.1, 30.12.0.a.2, 85.12.0.?, 102.2.0.?, 340.24.0.?, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.r1 |
13872bc1 |
13872.r |
13872bc |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{14} \cdot 3 \cdot 17^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$2.001169188$ |
$1$ |
|
$2$ |
$12096$ |
$0.524738$ |
$-289/12$ |
$1.03664$ |
$3.10393$ |
$1$ |
$[0, -1, 0, -96, -3072]$ |
\(y^2=x^3-x^2-96x-3072\) |
6.2.0.a.1 |
$[(32, 160)]$ |
$1$ |
| 13872.s1 |
13872y1 |
13872.s |
13872y |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{14} \cdot 3^{2} \cdot 17^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$55296$ |
$1.346226$ |
$1771561/612$ |
$1.28490$ |
$4.16292$ |
$1$ |
$[0, -1, 0, -11656, -303632]$ |
\(y^2=x^3-x^2-11656x-303632\) |
2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.? |
$[ ]$ |
$1$ |
| 13872.s2 |
13872y2 |
13872.s |
13872y |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{13} \cdot 3^{4} \cdot 17^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$136$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$110592$ |
$1.692799$ |
$46268279/46818$ |
$0.94894$ |
$4.50500$ |
$1$ |
$[0, -1, 0, 34584, -2153232]$ |
\(y^2=x^3-x^2+34584x-2153232\) |
2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.? |
$[ ]$ |
$1$ |
| 13872.t1 |
13872g1 |
13872.t |
13872g |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{10} \cdot 3^{9} \cdot 17^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$264384$ |
$1.969412$ |
$23324/19683$ |
$1.09674$ |
$4.92143$ |
$1$ |
$[0, -1, 0, 11464, 18030528]$ |
\(y^2=x^3-x^2+11464x+18030528\) |
6.2.0.a.1 |
$[ ]$ |
$1$ |
| 13872.u1 |
13872p1 |
13872.u |
13872p |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{10} \cdot 3^{9} \cdot 17^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.155122232$ |
$1$ |
|
$26$ |
$15552$ |
$0.552806$ |
$23324/19683$ |
$1.09674$ |
$3.13909$ |
$1$ |
$[0, 1, 0, 40, 3684]$ |
\(y^2=x^3+x^2+40x+3684\) |
6.2.0.a.1 |
$[(-8, 54), (10, 72)]$ |
$1$ |
| 13872.v1 |
13872bo1 |
13872.v |
13872bo |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{14} \cdot 3 \cdot 17^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$7.341921320$ |
$1$ |
|
$2$ |
$205632$ |
$1.941345$ |
$-289/12$ |
$1.03664$ |
$4.88626$ |
$1$ |
$[0, 1, 0, -27840, -15259596]$ |
\(y^2=x^3+x^2-27840x-15259596\) |
6.2.0.a.1 |
$[(8570, 793248)]$ |
$1$ |
| 13872.w1 |
13872bn2 |
13872.w |
13872bn |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{12} \cdot 3 \cdot 17^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$204$ |
$16$ |
$0$ |
$1.876064906$ |
$1$ |
|
$0$ |
$124416$ |
$1.850531$ |
$-23100424192/14739$ |
$1.03897$ |
$5.15655$ |
$1$ |
$[0, 1, 0, -274357, 55251491]$ |
\(y^2=x^3+x^2-274357x+55251491\) |
3.4.0.a.1, 12.8.0-3.a.1.3, 102.8.0.?, 204.16.0.? |
$[(2734/3, 4913/3)]$ |
$1$ |
| 13872.w2 |
13872bn1 |
13872.w |
13872bn |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{12} \cdot 3^{3} \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$204$ |
$16$ |
$0$ |
$0.625354968$ |
$1$ |
|
$2$ |
$41472$ |
$1.301224$ |
$32768/459$ |
$1.01165$ |
$4.07424$ |
$1$ |
$[0, 1, 0, 3083, 318371]$ |
\(y^2=x^3+x^2+3083x+318371\) |
3.4.0.a.1, 12.8.0-3.a.1.4, 102.8.0.?, 204.16.0.? |
$[(62, 867)]$ |
$1$ |
| 13872.x1 |
13872bm2 |
13872.x |
13872bm |
$2$ |
$5$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{12} \cdot 3^{5} \cdot 17^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$1020$ |
$48$ |
$1$ |
$1.500502029$ |
$1$ |
|
$2$ |
$326400$ |
$2.402630$ |
$-13549359104/243$ |
$1.07715$ |
$5.99167$ |
$1$ |
$[0, 1, 0, -3904197, 2967987699]$ |
\(y^2=x^3+x^2-3904197x+2967987699\) |
5.6.0.a.1, 30.12.0.a.1, 85.12.0.?, 102.2.0.?, 340.24.0.?, $\ldots$ |
$[(1830, 44217)]$ |
$1$ |
| 13872.x2 |
13872bm1 |
13872.x |
13872bm |
$2$ |
$5$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{12} \cdot 3 \cdot 17^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$1020$ |
$48$ |
$1$ |
$7.502510146$ |
$1$ |
|
$0$ |
$65280$ |
$1.597910$ |
$4096/3$ |
$0.95016$ |
$4.41771$ |
$1$ |
$[0, 1, 0, 26203, 850131]$ |
\(y^2=x^3+x^2+26203x+850131\) |
5.6.0.a.1, 30.12.0.a.2, 85.12.0.?, 102.2.0.?, 340.24.0.?, $\ldots$ |
$[(-13826/27, 11589767/27)]$ |
$1$ |
| 13872.y1 |
13872m3 |
13872.y |
13872m |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{11} \cdot 3^{8} \cdot 17^{7} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.54 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$147456$ |
$1.868912$ |
$22994537186/111537$ |
$1.03807$ |
$5.08328$ |
$1$ |
$[0, 1, 0, -217424, 38785716]$ |
\(y^2=x^3+x^2-217424x+38785716\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.8, 136.48.0.? |
$[ ]$ |
$1$ |
| 13872.y2 |
13872m2 |
13872.y |
13872m |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.6 |
2Cs |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$73728$ |
$1.522337$ |
$40873252/23409$ |
$1.13826$ |
$4.34665$ |
$1$ |
$[0, 1, 0, -20904, -125244]$ |
\(y^2=x^3+x^2-20904x-125244\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.3, 68.24.0-68.b.1.2, 136.48.0.? |
$[ ]$ |
$1$ |
| 13872.y3 |
13872m1 |
13872.y |
13872m |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 17^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.64 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$36864$ |
$1.175764$ |
$61918288/153$ |
$0.87866$ |
$4.24485$ |
$2$ |
$[0, 1, 0, -15124, -719428]$ |
\(y^2=x^3+x^2-15124x-719428\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.6, 34.6.0.a.1, 68.24.0-68.g.1.1, $\ldots$ |
$[ ]$ |
$1$ |
| 13872.y4 |
13872m4 |
13872.y |
13872m |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{11} \cdot 3^{2} \cdot 17^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.106 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$147456$ |
$1.868912$ |
$1285471294/751689$ |
$1.05433$ |
$4.78088$ |
$2$ |
$[0, 1, 0, 83136, -915948]$ |
\(y^2=x^3+x^2+83136x-915948\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.d.1.3, 68.12.0-4.c.1.2, 136.48.0.? |
$[ ]$ |
$1$ |
| 13872.z1 |
13872bp1 |
13872.z |
13872bp |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{19} \cdot 3 \cdot 17^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$102816$ |
$1.757435$ |
$5831/384$ |
$1.01027$ |
$4.65315$ |
$1$ |
$[0, 1, 0, 11464, 5021268]$ |
\(y^2=x^3+x^2+11464x+5021268\) |
24.2.0.b.1 |
$[ ]$ |
$1$ |
| 13872.ba1 |
13872bh1 |
13872.ba |
13872bh |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{8} \cdot 3^{7} \cdot 17^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1.134221132$ |
$1$ |
|
$4$ |
$91392$ |
$1.907085$ |
$-8192/2187$ |
$1.26266$ |
$4.84306$ |
$1$ |
$[0, 1, 0, -13101, -12414969]$ |
\(y^2=x^3+x^2-13101x-12414969\) |
102.2.0.? |
$[(963, 29478)]$ |
$1$ |
| 13872.bb1 |
13872bg1 |
13872.bb |
13872bg |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{8} \cdot 3 \cdot 17^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1.551229868$ |
$1$ |
|
$2$ |
$13824$ |
$0.905065$ |
$-65536/51$ |
$1.18457$ |
$3.61589$ |
$1$ |
$[0, 1, 0, -1541, 35151]$ |
\(y^2=x^3+x^2-1541x+35151\) |
102.2.0.? |
$[(147, 1734)]$ |
$1$ |
| 13872.bc1 |
13872l1 |
13872.bc |
13872l |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{11} \cdot 3^{3} \cdot 17^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$220320$ |
$2.235134$ |
$-68001122/27$ |
$1.13780$ |
$5.66100$ |
$1$ |
$[0, 1, 0, -1364176, -613938124]$ |
\(y^2=x^3+x^2-1364176x-613938124\) |
24.2.0.b.1 |
$[ ]$ |
$1$ |
| 13872.bd1 |
13872j1 |
13872.bd |
13872j |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{4} \cdot 3^{11} \cdot 17^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$269280$ |
$2.287285$ |
$-73984000/177147$ |
$1.11146$ |
$5.33263$ |
$1$ |
$[0, 1, 0, -278403, 128062440]$ |
\(y^2=x^3+x^2-278403x+128062440\) |
6.2.0.a.1 |
$[ ]$ |
$1$ |
| 13872.be1 |
13872bd2 |
13872.be |
13872bd |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{30} \cdot 3 \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$612$ |
$48$ |
$0$ |
$1.652918102$ |
$1$ |
|
$0$ |
$15552$ |
$1.025070$ |
$-4999353625/786432$ |
$1.12790$ |
$3.83295$ |
$1$ |
$[0, 1, 0, -3768, 99156]$ |
\(y^2=x^3+x^2-3768x+99156\) |
3.4.0.a.1, 6.8.0.b.1, 18.24.0.c.1, 204.16.0.?, 612.48.0.? |
$[(406/3, 4096/3)]$ |
$1$ |
| 13872.be2 |
13872bd1 |
13872.be |
13872bd |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17^{2} \) |
\( - 2^{18} \cdot 3^{3} \cdot 17^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$204$ |
$48$ |
$0$ |
$0.550972700$ |
$1$ |
|
$4$ |
$5184$ |
$0.475765$ |
$2828375/1728$ |
$1.02006$ |
$3.02375$ |
$1$ |
$[0, 1, 0, 312, -396]$ |
\(y^2=x^3+x^2+312x-396\) |
3.4.0.a.1, 6.24.0.c.1, 204.48.0.? |
$[(30, 192)]$ |
$1$ |
