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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
1078.a1 |
1078b1 |
1078.a |
1078b |
$1$ |
$1$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{9} \cdot 7^{8} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$88$ |
$2$ |
$0$ |
$2.500935374$ |
$1$ |
|
$2$ |
$6048$ |
$1.175161$ |
$551516475321/5632$ |
$[1, -1, 0, -30634, -2056076]$ |
\(y^2+xy=x^3-x^2-30634x-2056076\) |
88.2.0.? |
$[(-101, 53)]$ |
1078.b1 |
1078f2 |
1078.b |
1078f |
$2$ |
$2$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{2} \cdot 7^{8} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$0.426448232$ |
$1$ |
|
$8$ |
$1536$ |
$0.880641$ |
$1426487591593/2156$ |
$[1, 0, 1, -11492, 473190]$ |
\(y^2+xy+y=x^3-11492x+473190\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.? |
$[(60, -6)]$ |
1078.b2 |
1078f1 |
1078.b |
1078f |
$2$ |
$2$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( - 2^{4} \cdot 7^{7} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$0.213224116$ |
$1$ |
|
$13$ |
$768$ |
$0.534067$ |
$-338608873/13552$ |
$[1, 0, 1, -712, 7494]$ |
\(y^2+xy+y=x^3-712x+7494\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.? |
$[(-3, 99)]$ |
1078.c1 |
1078d2 |
1078.c |
1078d |
$2$ |
$3$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{3} \cdot 7^{10} \cdot 11^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$1848$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$2016$ |
$1.206627$ |
$911871625/10648$ |
$[1, 1, 0, -13255, 575933]$ |
\(y^2+xy=x^3+x^2-13255x+575933\) |
3.4.0.a.1, 21.8.0-3.a.1.2, 88.2.0.?, 264.8.0.?, 1848.16.0.? |
$[]$ |
1078.c2 |
1078d1 |
1078.c |
1078d |
$2$ |
$3$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2 \cdot 7^{10} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$1848$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$672$ |
$0.657322$ |
$765625/22$ |
$[1, 1, 0, -1250, -17114]$ |
\(y^2+xy=x^3+x^2-1250x-17114\) |
3.4.0.a.1, 21.8.0-3.a.1.1, 88.2.0.?, 264.8.0.?, 1848.16.0.? |
$[]$ |
1078.d1 |
1078c2 |
1078.d |
1078c |
$2$ |
$2$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{3} \cdot 7^{8} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$2304$ |
$1.020969$ |
$11422548526761/4312$ |
$[1, -1, 0, -22990, -1335972]$ |
\(y^2+xy=x^3-x^2-22990x-1335972\) |
2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.? |
$[]$ |
1078.d2 |
1078c1 |
1078.d |
1078c |
$2$ |
$2$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( - 2^{6} \cdot 7^{7} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1152$ |
$0.674397$ |
$-2749884201/54208$ |
$[1, -1, 0, -1430, -20812]$ |
\(y^2+xy=x^3-x^2-1430x-20812\) |
2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.? |
$[]$ |
1078.e1 |
1078a2 |
1078.e |
1078a |
$2$ |
$3$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{3} \cdot 7^{4} \cdot 11^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$264$ |
$16$ |
$0$ |
$0.607463566$ |
$1$ |
|
$4$ |
$288$ |
$0.233673$ |
$911871625/10648$ |
$[1, 0, 1, -271, -1718]$ |
\(y^2+xy+y=x^3-271x-1718\) |
3.8.0-3.a.1.1, 88.2.0.?, 264.16.0.? |
$[(-10, 8)]$ |
1078.e2 |
1078a1 |
1078.e |
1078a |
$2$ |
$3$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2 \cdot 7^{4} \cdot 11 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$264$ |
$16$ |
$0$ |
$1.822390698$ |
$1$ |
|
$4$ |
$96$ |
$-0.315633$ |
$765625/22$ |
$[1, 0, 1, -26, 46]$ |
\(y^2+xy+y=x^3-26x+46\) |
3.8.0-3.a.1.2, 88.2.0.?, 264.16.0.? |
$[(-2, 10)]$ |
1078.f1 |
1078e1 |
1078.f |
1078e |
$1$ |
$1$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{9} \cdot 7^{2} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$88$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$864$ |
$0.202207$ |
$551516475321/5632$ |
$[1, -1, 0, -625, 6173]$ |
\(y^2+xy=x^3-x^2-625x+6173\) |
88.2.0.? |
$[]$ |
1078.g1 |
1078k1 |
1078.g |
1078k |
$1$ |
$1$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{3} \cdot 7^{2} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$88$ |
$2$ |
$0$ |
$0.234909178$ |
$1$ |
|
$6$ |
$144$ |
$-0.588044$ |
$415233/88$ |
$[1, -1, 1, -6, -3]$ |
\(y^2+xy+y=x^3-x^2-6x-3\) |
88.2.0.? |
$[(-1, 1)]$ |
1078.h1 |
1078m2 |
1078.h |
1078m |
$2$ |
$2$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2 \cdot 7^{9} \cdot 11^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.3 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1792$ |
$1.009790$ |
$59776471/29282$ |
$[1, 0, 0, -2794, -22506]$ |
\(y^2+xy=x^3-2794x-22506\) |
2.3.0.a.1, 8.6.0.e.1, 28.6.0.c.1, 56.12.0.bd.1 |
$[]$ |
1078.h2 |
1078m1 |
1078.h |
1078m |
$2$ |
$2$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( - 2^{2} \cdot 7^{9} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.3 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$896$ |
$0.663217$ |
$704969/484$ |
$[1, 0, 0, 636, -2612]$ |
\(y^2+xy=x^3+636x-2612\) |
2.3.0.a.1, 8.6.0.e.1, 14.6.0.b.1, 56.12.0.bc.1 |
$[]$ |
1078.i1 |
1078j2 |
1078.i |
1078j |
$2$ |
$3$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{5} \cdot 7^{2} \cdot 11^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$1848$ |
$16$ |
$0$ |
$0.297078670$ |
$1$ |
|
$6$ |
$720$ |
$0.642303$ |
$413160293352625/42592$ |
$[1, 1, 1, -5678, 162315]$ |
\(y^2+xy+y=x^3+x^2-5678x+162315\) |
3.4.0.a.1, 21.8.0-3.a.1.2, 88.2.0.?, 264.8.0.?, 1848.16.0.? |
$[(43, -21)]$ |
1078.i2 |
1078j1 |
1078.i |
1078j |
$2$ |
$3$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{15} \cdot 7^{2} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$1848$ |
$16$ |
$0$ |
$0.099026223$ |
$1$ |
|
$10$ |
$240$ |
$0.092997$ |
$1071912625/360448$ |
$[1, 1, 1, -78, 139]$ |
\(y^2+xy+y=x^3+x^2-78x+139\) |
3.4.0.a.1, 21.8.0-3.a.1.1, 88.2.0.?, 264.8.0.?, 1848.16.0.? |
$[(1, 7)]$ |
1078.j1 |
1078i4 |
1078.j |
1078i |
$4$ |
$4$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{3} \cdot 7^{10} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.105 |
2B |
$56$ |
$48$ |
$0$ |
$0.687446525$ |
$1$ |
|
$6$ |
$4608$ |
$1.600128$ |
$15226621995131793/2324168$ |
$[1, -1, 1, -253021, 49050397]$ |
\(y^2+xy+y=x^3-x^2-253021x+49050397\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.k.1.3, 28.12.0-4.c.1.1, 56.48.0-56.v.1.4 |
$[(289, -96)]$ |
1078.j2 |
1078i3 |
1078.j |
1078i |
$4$ |
$4$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{3} \cdot 7^{7} \cdot 11^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.61 |
2B |
$56$ |
$48$ |
$0$ |
$2.749786103$ |
$1$ |
|
$2$ |
$4608$ |
$1.600128$ |
$24331017010833/12004097336$ |
$[1, -1, 1, -29581, -744579]$ |
\(y^2+xy+y=x^3-x^2-29581x-744579\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.6, 56.48.0-56.bp.1.8 |
$[(-47, 758)]$ |
1078.j3 |
1078i2 |
1078.j |
1078i |
$4$ |
$4$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{6} \cdot 7^{8} \cdot 11^{4} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.5 |
2Cs |
$56$ |
$48$ |
$0$ |
$1.374893051$ |
$1$ |
|
$8$ |
$2304$ |
$1.253555$ |
$3750606459153/45914176$ |
$[1, -1, 1, -15861, 764621]$ |
\(y^2+xy+y=x^3-x^2-15861x+764621\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.3, 28.24.0-28.b.1.1, 56.48.0-56.d.1.2 |
$[(97, 314)]$ |
1078.j4 |
1078i1 |
1078.j |
1078i |
$4$ |
$4$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( - 2^{12} \cdot 7^{7} \cdot 11^{2} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.51 |
2B |
$56$ |
$48$ |
$0$ |
$0.687446525$ |
$1$ |
|
$15$ |
$1152$ |
$0.906981$ |
$-5545233/3469312$ |
$[1, -1, 1, -181, 30797]$ |
\(y^2+xy+y=x^3-x^2-181x+30797\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.8, 14.6.0.b.1, 28.24.0-28.g.1.2, $\ldots$ |
$[(-1, 176)]$ |
1078.k1 |
1078g2 |
1078.k |
1078g |
$2$ |
$3$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{5} \cdot 7^{8} \cdot 11^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$264$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5040$ |
$1.615259$ |
$413160293352625/42592$ |
$[1, 0, 0, -278223, -56508775]$ |
\(y^2+xy=x^3-278223x-56508775\) |
3.8.0-3.a.1.1, 88.2.0.?, 264.16.0.? |
$[]$ |
1078.k2 |
1078g1 |
1078.k |
1078g |
$2$ |
$3$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{15} \cdot 7^{8} \cdot 11 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$264$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$1680$ |
$1.065952$ |
$1071912625/360448$ |
$[1, 0, 0, -3823, -59207]$ |
\(y^2+xy=x^3-3823x-59207\) |
3.8.0-3.a.1.2, 88.2.0.?, 264.16.0.? |
$[]$ |
1078.l1 |
1078l2 |
1078.l |
1078l |
$2$ |
$2$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2 \cdot 7^{3} \cdot 11^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.3 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$256$ |
$0.036835$ |
$59776471/29282$ |
$[1, 1, 1, -57, 41]$ |
\(y^2+xy+y=x^3+x^2-57x+41\) |
2.3.0.a.1, 8.6.0.e.1, 28.6.0.c.1, 56.12.0.bd.1 |
$[]$ |
1078.l2 |
1078l1 |
1078.l |
1078l |
$2$ |
$2$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( - 2^{2} \cdot 7^{3} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.3 |
2B |
$56$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$128$ |
$-0.309739$ |
$704969/484$ |
$[1, 1, 1, 13, 13]$ |
\(y^2+xy+y=x^3+x^2+13x+13\) |
2.3.0.a.1, 8.6.0.e.1, 14.6.0.b.1, 56.12.0.bc.1 |
$[]$ |
1078.m1 |
1078h1 |
1078.m |
1078h |
$1$ |
$1$ |
\( 2 \cdot 7^{2} \cdot 11 \) |
\( 2^{3} \cdot 7^{8} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$88$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1008$ |
$0.384911$ |
$415233/88$ |
$[1, -1, 1, -279, 1495]$ |
\(y^2+xy+y=x^3-x^2-279x+1495\) |
88.2.0.? |
$[]$ |