| 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 |
Manin constant |
| 10086.a1 |
10086c1 |
10086.a |
10086c |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{14} \cdot 3^{12} \cdot 41^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$328$ |
$12$ |
$0$ |
$28.94792104$ |
$1$ |
|
$1$ |
$2822400$ |
$3.571167$ |
$10341755683137709164937/356992303104$ |
$1.06164$ |
$7.91547$ |
$[1, 1, 0, -763000051, -8112448846355]$ |
\(y^2+xy=x^3+x^2-763000051x-8112448846355\) |
2.3.0.a.1, 8.6.0.d.1, 82.6.0.?, 328.12.0.? |
$[(-3464536698407003/466057, 784001395068712236772/466057)]$ |
$1$ |
| 10086.a2 |
10086c2 |
10086.a |
10086c |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{7} \cdot 3^{24} \cdot 41^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$328$ |
$12$ |
$0$ |
$57.89584208$ |
$1$ |
|
$0$ |
$5644800$ |
$3.917740$ |
$-10298071306410575356297/60769798505543808$ |
$1.06173$ |
$7.91611$ |
$[1, 1, 0, -761924211, -8136465253011]$ |
\(y^2+xy=x^3+x^2-761924211x-8136465253011\) |
2.3.0.a.1, 8.6.0.a.1, 164.6.0.?, 328.12.0.? |
$[(3585062769762460819537190531/66744525541, 214409587426192562146854014781413999069880/66744525541)]$ |
$1$ |
| 10086.b1 |
10086b1 |
10086.b |
10086b |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{16} \cdot 3^{3} \cdot 41^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$12$ |
$2$ |
$0$ |
$0.689120704$ |
$1$ |
|
$4$ |
$8064$ |
$0.611083$ |
$92806423177/1769472$ |
$0.99835$ |
$3.54499$ |
$[1, 1, 0, -1121, 13749]$ |
\(y^2+xy=x^3+x^2-1121x+13749\) |
12.2.0.a.1 |
$[(34, 111)]$ |
$1$ |
| 10086.c1 |
10086a1 |
10086.c |
10086a |
$2$ |
$5$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{5} \cdot 3^{3} \cdot 41^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$4920$ |
$48$ |
$1$ |
$0.574713453$ |
$1$ |
|
$4$ |
$2400$ |
$0.233682$ |
$-9129329/864$ |
$0.94721$ |
$2.96339$ |
$[1, 1, 0, -178, 916]$ |
\(y^2+xy=x^3+x^2-178x+916\) |
5.6.0.a.1, 120.12.0.?, 205.24.0.?, 984.2.0.?, 4920.48.1.? |
$[(3, 19)]$ |
$1$ |
| 10086.c2 |
10086a2 |
10086.c |
10086a |
$2$ |
$5$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2 \cdot 3^{15} \cdot 41^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$4920$ |
$48$ |
$1$ |
$2.873567265$ |
$1$ |
|
$2$ |
$12000$ |
$1.038401$ |
$19902511/28697814$ |
$1.14205$ |
$3.87979$ |
$[1, 1, 0, 232, -67554]$ |
\(y^2+xy=x^3+x^2+232x-67554\) |
5.6.0.a.1, 120.12.0.?, 205.24.0.?, 984.2.0.?, 4920.48.1.? |
$[(85, 716)]$ |
$1$ |
| 10086.d1 |
10086e1 |
10086.d |
10086e |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{4} \cdot 3^{5} \cdot 41^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$12$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$137760$ |
$1.866274$ |
$11259625/3888$ |
$0.93616$ |
$4.98382$ |
$[1, 1, 0, -93330, -7008444]$ |
\(y^2+xy=x^3+x^2-93330x-7008444\) |
12.2.0.a.1 |
$[ ]$ |
$1$ |
| 10086.e1 |
10086f1 |
10086.e |
10086f |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{9} \cdot 3^{5} \cdot 41^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$154980$ |
$2.216278$ |
$-2643729241/124416$ |
$0.97264$ |
$5.58442$ |
$[1, 1, 0, -575777, -175106763]$ |
\(y^2+xy=x^3+x^2-575777x-175106763\) |
24.2.0.b.1 |
$[ ]$ |
$1$ |
| 10086.f1 |
10086d1 |
10086.f |
10086d |
$2$ |
$3$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2 \cdot 3^{3} \cdot 41^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$984$ |
$16$ |
$0$ |
$1.369364306$ |
$1$ |
|
$0$ |
$33600$ |
$1.182581$ |
$-389017/2214$ |
$0.87552$ |
$4.07158$ |
$[1, 1, 0, -2556, 162702]$ |
\(y^2+xy=x^3+x^2-2556x+162702\) |
3.4.0.a.1, 24.8.0-3.a.1.5, 123.8.0.?, 984.16.0.? |
$[(-193/2, 3555/2)]$ |
$1$ |
| 10086.f2 |
10086d2 |
10086.f |
10086d |
$2$ |
$3$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{3} \cdot 3 \cdot 41^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$984$ |
$16$ |
$0$ |
$4.108092920$ |
$1$ |
|
$0$ |
$100800$ |
$1.731888$ |
$270840023/1654104$ |
$0.95436$ |
$4.76796$ |
$[1, 1, 0, 22659, -4048203]$ |
\(y^2+xy=x^3+x^2+22659x-4048203\) |
3.4.0.a.1, 24.8.0-3.a.1.6, 123.8.0.?, 984.16.0.? |
$[(28631/10, 4956999/10)]$ |
$1$ |
| 10086.g1 |
10086j1 |
10086.g |
10086j |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{6} \cdot 3^{4} \cdot 41^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$328$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$80640$ |
$1.714922$ |
$32553430057/212544$ |
$0.94292$ |
$5.04264$ |
$[1, 0, 1, -111822, 14301760]$ |
\(y^2+xy+y=x^3-111822x+14301760\) |
2.3.0.a.1, 8.6.0.d.1, 82.6.0.?, 328.12.0.? |
$[ ]$ |
$1$ |
| 10086.g2 |
10086j2 |
10086.g |
10086j |
$2$ |
$2$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{3} \cdot 3^{8} \cdot 41^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$328$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$161280$ |
$2.061497$ |
$-2062933417/88232328$ |
$1.00890$ |
$5.21158$ |
$[1, 0, 1, -44582, 31353824]$ |
\(y^2+xy+y=x^3-44582x+31353824\) |
2.3.0.a.1, 8.6.0.a.1, 164.6.0.?, 328.12.0.? |
$[ ]$ |
$1$ |
| 10086.h1 |
10086l1 |
10086.h |
10086l |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{16} \cdot 3^{3} \cdot 41^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$12$ |
$2$ |
$0$ |
$0.933381210$ |
$1$ |
|
$2$ |
$330624$ |
$2.467869$ |
$92806423177/1769472$ |
$0.99835$ |
$5.96192$ |
$[1, 0, 1, -1885277, 979639544]$ |
\(y^2+xy+y=x^3-1885277x+979639544\) |
12.2.0.a.1 |
$[(11907, 1285054)]$ |
$1$ |
| 10086.i1 |
10086i1 |
10086.i |
10086i |
$2$ |
$5$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{5} \cdot 3^{3} \cdot 41^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$4920$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$98400$ |
$2.090469$ |
$-9129329/864$ |
$0.94721$ |
$5.38032$ |
$[1, 0, 1, -300094, 68228240]$ |
\(y^2+xy+y=x^3-300094x+68228240\) |
5.6.0.a.1, 120.12.0.?, 205.24.0.?, 984.2.0.?, 4920.48.1.? |
$[ ]$ |
$1$ |
| 10086.i2 |
10086i2 |
10086.i |
10086i |
$2$ |
$5$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2 \cdot 3^{15} \cdot 41^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$4920$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$492000$ |
$2.895187$ |
$19902511/28697814$ |
$1.14205$ |
$6.29671$ |
$[1, 0, 1, 389116, -4662509200]$ |
\(y^2+xy+y=x^3+389116x-4662509200\) |
5.6.0.a.1, 120.12.0.?, 205.24.0.?, 984.2.0.?, 4920.48.1.? |
$[ ]$ |
$1$ |
| 10086.j1 |
10086g1 |
10086.j |
10086g |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{4} \cdot 3^{5} \cdot 41^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$12$ |
$2$ |
$0$ |
$0.265735699$ |
$1$ |
|
$18$ |
$3360$ |
$0.009488$ |
$11259625/3888$ |
$0.93616$ |
$2.56689$ |
$[1, 0, 1, -56, -106]$ |
\(y^2+xy+y=x^3-56x-106\) |
12.2.0.a.1 |
$[(-3, 7), (-6, 7)]$ |
$1$ |
| 10086.k1 |
10086h1 |
10086.k |
10086h |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{9} \cdot 3^{5} \cdot 41^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$24$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3780$ |
$0.359491$ |
$-2643729241/124416$ |
$0.97264$ |
$3.16749$ |
$[1, 0, 1, -343, -2566]$ |
\(y^2+xy+y=x^3-343x-2566\) |
24.2.0.b.1 |
$[ ]$ |
$1$ |
| 10086.l1 |
10086k1 |
10086.l |
10086k |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{11} \cdot 3 \cdot 41^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$984$ |
$2$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$73920$ |
$1.669195$ |
$-7916293657/251904$ |
$0.93151$ |
$4.89507$ |
$[1, 0, 1, -69797, -7295728]$ |
\(y^2+xy+y=x^3-69797x-7295728\) |
984.2.0.? |
$[ ]$ |
$1$ |
| 10086.m1 |
10086n3 |
10086.m |
10086n |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2 \cdot 3^{8} \cdot 41^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.64 |
2B |
$328$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$161280$ |
$2.019928$ |
$9357915116017/538002$ |
$0.98265$ |
$5.65671$ |
$[1, 1, 1, -737994, -244316475]$ |
\(y^2+xy+y=x^3+x^2-737994x-244316475\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.6, 328.48.0.? |
$[ ]$ |
$1$ |
| 10086.m2 |
10086n2 |
10086.m |
10086n |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{2} \cdot 3^{4} \cdot 41^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.6 |
2Cs |
$328$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$2$ |
$80640$ |
$1.673355$ |
$2703045457/544644$ |
$0.99714$ |
$4.77270$ |
$[1, 1, 1, -48784, -3368659]$ |
\(y^2+xy+y=x^3+x^2-48784x-3368659\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.3, 164.24.0.?, 328.48.0.? |
$[ ]$ |
$1$ |
| 10086.m3 |
10086n1 |
10086.m |
10086n |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{4} \cdot 3^{2} \cdot 41^{7} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.54 |
2B |
$328$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$40320$ |
$1.326780$ |
$81182737/5904$ |
$0.95826$ |
$4.39246$ |
$[1, 1, 1, -15164, 665741]$ |
\(y^2+xy+y=x^3+x^2-15164x+665741\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.m.1.8, 82.6.0.?, 164.24.0.?, $\ldots$ |
$[ ]$ |
$1$ |
| 10086.m4 |
10086n4 |
10086.m |
10086n |
$4$ |
$4$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2 \cdot 3^{2} \cdot 41^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.106 |
2B |
$328$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$161280$ |
$2.019928$ |
$25076571983/50863698$ |
$0.97224$ |
$5.11394$ |
$[1, 1, 1, 102506, -19950043]$ |
\(y^2+xy+y=x^3+x^2+102506x-19950043\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.d.1.3, 164.12.0.?, 328.48.0.? |
$[ ]$ |
$1$ |
| 10086.n1 |
10086o1 |
10086.n |
10086o |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{12} \cdot 3^{11} \cdot 41^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$12$ |
$2$ |
$0$ |
$1.085986079$ |
$1$ |
|
$2$ |
$909216$ |
$3.082333$ |
$549464024729857/725594112$ |
$1.04271$ |
$6.90413$ |
$[1, 1, 1, -34105844, 76562241077]$ |
\(y^2+xy+y=x^3+x^2-34105844x+76562241077\) |
12.2.0.a.1 |
$[(2381, 92945)]$ |
$1$ |
| 10086.o1 |
10086m2 |
10086.o |
10086m |
$2$ |
$5$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{5} \cdot 3 \cdot 41^{11} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$4920$ |
$48$ |
$1$ |
$1$ |
$25$ |
$5$ |
$0$ |
$2520000$ |
$3.551865$ |
$-21525971829968662032241/11122195296$ |
$1.06339$ |
$7.99498$ |
$[1, 1, 1, -974198370, -11703998947377]$ |
\(y^2+xy+y=x^3+x^2-974198370x-11703998947377\) |
5.12.0.a.2, 120.24.0.?, 205.24.0.?, 984.2.0.?, 4920.48.1.? |
$[ ]$ |
$1$ |
| 10086.o2 |
10086m1 |
10086.o |
10086m |
$2$ |
$5$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{25} \cdot 3^{5} \cdot 41^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$4920$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$504000$ |
$2.747147$ |
$-592915705201/334302806016$ |
$1.07782$ |
$6.10403$ |
$[1, 1, 1, -294210, -1918360497]$ |
\(y^2+xy+y=x^3+x^2-294210x-1918360497\) |
5.12.0.a.1, 120.24.0.?, 205.24.0.?, 984.2.0.?, 4920.48.1.? |
$[ ]$ |
$1$ |
| 10086.p1 |
10086q1 |
10086.p |
10086q |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( 2^{12} \cdot 3^{11} \cdot 41^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$12$ |
$2$ |
$0$ |
$0.059071790$ |
$1$ |
|
$12$ |
$22176$ |
$1.225548$ |
$549464024729857/725594112$ |
$1.04271$ |
$4.48720$ |
$[1, 0, 0, -20289, 1109385]$ |
\(y^2+xy=x^3-20289x+1109385\) |
12.2.0.a.1 |
$[(78, 15)]$ |
$1$ |
| 10086.q1 |
10086p1 |
10086.q |
10086p |
$1$ |
$1$ |
\( 2 \cdot 3 \cdot 41^{2} \) |
\( - 2^{3} \cdot 3^{7} \cdot 41^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$984$ |
$2$ |
$0$ |
$1.031837211$ |
$1$ |
|
$4$ |
$141120$ |
$1.953739$ |
$-2177286259681/717336$ |
$0.97361$ |
$5.49860$ |
$[1, 0, 0, -453905, -117776511]$ |
\(y^2+xy=x^3-453905x-117776511\) |
984.2.0.? |
$[(796, 4645)]$ |
$1$ |
