| 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 |
| 17784.a1 |
17784d1 |
17784.a |
17784d |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{10} \cdot 3^{11} \cdot 13 \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2964$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$20480$ |
$0.732796$ |
$94559612/60021$ |
$0.84166$ |
$3.25850$ |
$[0, 0, 0, 861, -3026]$ |
\(y^2=x^3+861x-3026\) |
2964.2.0.? |
$[ ]$ |
| 17784.b1 |
17784i1 |
17784.b |
17784i |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( 2^{4} \cdot 3^{3} \cdot 13 \cdot 19 \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$2964$ |
$12$ |
$0$ |
$1.896590072$ |
$1$ |
|
$11$ |
$3328$ |
$0.021945$ |
$3811055616/247$ |
$0.97233$ |
$2.87446$ |
$[0, 0, 0, -246, 1485]$ |
\(y^2=x^3-246x+1485\) |
2.3.0.a.1, 12.6.0.c.1, 988.6.0.?, 1482.6.0.?, 2964.12.0.? |
$[(6, 15), (13, 22)]$ |
| 17784.b2 |
17784i2 |
17784.b |
17784i |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{8} \cdot 3^{3} \cdot 13^{2} \cdot 19^{2} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$2964$ |
$12$ |
$0$ |
$0.474147518$ |
$1$ |
|
$23$ |
$6656$ |
$0.368519$ |
$-197222256/61009$ |
$0.89261$ |
$2.89893$ |
$[0, 0, 0, -231, 1674]$ |
\(y^2=x^3-231x+1674\) |
2.3.0.a.1, 6.6.0.a.1, 988.6.0.?, 2964.12.0.? |
$[(1, 38), (-5, 52)]$ |
| 17784.c1 |
17784q3 |
17784.c |
17784q |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( 2^{10} \cdot 3^{26} \cdot 13 \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$5928$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$184320$ |
$2.109276$ |
$1677865892403172/861235747047$ |
$0.98251$ |
$4.96415$ |
$[0, 0, 0, -224571, 13771366]$ |
\(y^2=x^3-224571x+13771366\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.z.1.4, $\ldots$ |
$[ ]$ |
| 17784.c2 |
17784q2 |
17784.c |
17784q |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( 2^{8} \cdot 3^{16} \cdot 13^{2} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$2964$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$92160$ |
$1.762701$ |
$3462397543530448/3602520441$ |
$1.00447$ |
$4.89652$ |
$[0, 0, 0, -180111, 29394610]$ |
\(y^2=x^3-180111x+29394610\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 988.24.0.?, 2964.48.0.? |
$[ ]$ |
| 17784.c3 |
17784q1 |
17784.c |
17784q |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( 2^{4} \cdot 3^{11} \cdot 13 \cdot 19 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$5928$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$3$ |
$46080$ |
$1.416128$ |
$55356847905445888/60021$ |
$1.04663$ |
$4.89644$ |
$[0, 0, 0, -180066, 29410045]$ |
\(y^2=x^3-180066x+29410045\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 1482.6.0.?, 1976.24.0.?, $\ldots$ |
$[ ]$ |
| 17784.c4 |
17784q4 |
17784.c |
17784q |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{10} \cdot 3^{11} \cdot 13^{4} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$5928$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$184320$ |
$2.109276$ |
$-375718260235972/904469833683$ |
$0.96798$ |
$4.97891$ |
$[0, 0, 0, -136371, 44030014]$ |
\(y^2=x^3-136371x+44030014\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 1976.24.0.?, $\ldots$ |
$[ ]$ |
| 17784.d1 |
17784m1 |
17784.d |
17784m |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{6} \cdot 13 \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$494$ |
$2$ |
$0$ |
$1.039505834$ |
$1$ |
|
$2$ |
$2560$ |
$-0.080609$ |
$6912/247$ |
$0.75459$ |
$2.27998$ |
$[0, 0, 0, 9, -81]$ |
\(y^2=x^3+9x-81\) |
494.2.0.? |
$[(9, 27)]$ |
| 17784.e1 |
17784j1 |
17784.e |
17784j |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{11} \cdot 3^{3} \cdot 13^{3} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$5928$ |
$2$ |
$0$ |
$1.009763130$ |
$1$ |
|
$2$ |
$8832$ |
$0.485111$ |
$59007258/41743$ |
$0.82787$ |
$2.94436$ |
$[0, 0, 0, 309, -986]$ |
\(y^2=x^3+309x-986\) |
5928.2.0.? |
$[(14, 78)]$ |
| 17784.f1 |
17784s1 |
17784.f |
17784s |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{8} \cdot 3^{8} \cdot 13^{4} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$0.349671943$ |
$1$ |
|
$6$ |
$20480$ |
$0.996993$ |
$-8069733376/4883931$ |
$0.86937$ |
$3.64437$ |
$[0, 0, 0, -2388, 64244]$ |
\(y^2=x^3-2388x+64244\) |
38.2.0.a.1 |
$[(4, 234)]$ |
| 17784.g1 |
17784f1 |
17784.g |
17784f |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{10} \cdot 3^{7} \cdot 13^{3} \cdot 19^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2964$ |
$2$ |
$0$ |
$0.348376100$ |
$1$ |
|
$6$ |
$36864$ |
$1.383682$ |
$-1987925163844/45207669$ |
$1.06708$ |
$4.27954$ |
$[0, 0, 0, -23763, 1437374]$ |
\(y^2=x^3-23763x+1437374\) |
2964.2.0.? |
$[(127, 684)]$ |
| 17784.h1 |
17784l1 |
17784.h |
17784l |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{11} \cdot 3^{23} \cdot 13 \cdot 19^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$5928$ |
$2$ |
$0$ |
$7.726209556$ |
$1$ |
|
$0$ |
$1109760$ |
$2.869919$ |
$-1762982669155531250/4156929770033781$ |
$1.04903$ |
$5.91189$ |
$[0, 0, 0, -2876475, 4229930806]$ |
\(y^2=x^3-2876475x+4229930806\) |
5928.2.0.? |
$[(628142/11, 478414998/11)]$ |
| 17784.i1 |
17784e1 |
17784.i |
17784e |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{6} \cdot 13 \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$494$ |
$2$ |
$0$ |
$0.493381186$ |
$1$ |
|
$4$ |
$1920$ |
$-0.006147$ |
$-4000000/247$ |
$0.76949$ |
$2.52067$ |
$[0, 0, 0, -75, 263]$ |
\(y^2=x^3-75x+263\) |
494.2.0.? |
$[(7, 9)]$ |
| 17784.j1 |
17784n1 |
17784.j |
17784n |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{12} \cdot 13^{3} \cdot 19^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$494$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$161280$ |
$2.048553$ |
$-859256706676000000/3965752347687$ |
$1.02664$ |
$5.17747$ |
$[0, 0, 0, -449175, -116331257]$ |
\(y^2=x^3-449175x-116331257\) |
494.2.0.? |
$[ ]$ |
| 17784.k1 |
17784k2 |
17784.k |
17784k |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( 2^{8} \cdot 3^{8} \cdot 13 \cdot 19^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$3.327792164$ |
$1$ |
|
$3$ |
$67584$ |
$1.504910$ |
$6772976019826000/42237$ |
$0.95227$ |
$4.96508$ |
$[0, 0, 0, -225255, -41149046]$ |
\(y^2=x^3-225255x-41149046\) |
2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.? |
$[(593, 5814)]$ |
| 17784.k2 |
17784k1 |
17784.k |
17784k |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{7} \cdot 13^{2} \cdot 19^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$6.655584328$ |
$1$ |
|
$3$ |
$33792$ |
$1.158335$ |
$-26409397504000/66072747$ |
$0.94071$ |
$4.11538$ |
$[0, 0, 0, -14070, -643763]$ |
\(y^2=x^3-14070x-643763\) |
2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.? |
$[(3894, 242879)]$ |
| 17784.l1 |
17784o1 |
17784.l |
17784o |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( 2^{4} \cdot 3^{24} \cdot 13 \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$460800$ |
$2.571926$ |
$1201953427358681344000/656357332110597$ |
$1.02901$ |
$5.91684$ |
$[0, 0, 0, -5023470, -4331604859]$ |
\(y^2=x^3-5023470x-4331604859\) |
2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.? |
$[ ]$ |
| 17784.l2 |
17784o2 |
17784.l |
17784o |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{8} \cdot 3^{15} \cdot 13^{2} \cdot 19^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$921600$ |
$2.918499$ |
$-41980174295570098000/56494582655784507$ |
$1.00851$ |
$5.98016$ |
$[0, 0, 0, -4137735, -5907681718]$ |
\(y^2=x^3-4137735x-5907681718\) |
2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.? |
$[ ]$ |
| 17784.m1 |
17784c1 |
17784.m |
17784c |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( 2^{4} \cdot 3^{16} \cdot 13 \cdot 19^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$35840$ |
$1.210625$ |
$22559008000000/277116957$ |
$0.99646$ |
$4.09883$ |
$[0, 0, 0, -13350, 587369]$ |
\(y^2=x^3-13350x+587369\) |
2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.? |
$[ ]$ |
| 17784.m2 |
17784c2 |
17784.m |
17784c |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{8} \cdot 3^{11} \cdot 13^{2} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$71680$ |
$1.557198$ |
$-8346562000/5351892507$ |
$0.98365$ |
$4.29113$ |
$[0, 0, 0, -2415, 1521218]$ |
\(y^2=x^3-2415x+1521218\) |
2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.? |
$[ ]$ |
| 17784.n1 |
17784h1 |
17784.n |
17784h |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{10} \cdot 3^{19} \cdot 13 \cdot 19^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2964$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$159744$ |
$1.962231$ |
$-136667088859396/142160998941$ |
$0.95285$ |
$4.81302$ |
$[0, 0, 0, -97347, 19553038]$ |
\(y^2=x^3-97347x+19553038\) |
2964.2.0.? |
$[ ]$ |
| 17784.o1 |
17784a1 |
17784.o |
17784a |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( 2^{4} \cdot 3^{9} \cdot 13 \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$2964$ |
$12$ |
$0$ |
$7.223771966$ |
$1$ |
|
$1$ |
$9984$ |
$0.571251$ |
$3811055616/247$ |
$0.97233$ |
$3.54804$ |
$[0, 0, 0, -2214, -40095]$ |
\(y^2=x^3-2214x-40095\) |
2.3.0.a.1, 12.6.0.c.1, 988.6.0.?, 1482.6.0.?, 2964.12.0.? |
$[(937/4, 11285/4)]$ |
| 17784.o2 |
17784a2 |
17784.o |
17784a |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{8} \cdot 3^{9} \cdot 13^{2} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$2964$ |
$12$ |
$0$ |
$3.611885983$ |
$1$ |
|
$3$ |
$19968$ |
$0.917825$ |
$-197222256/61009$ |
$0.89261$ |
$3.57251$ |
$[0, 0, 0, -2079, -45198]$ |
\(y^2=x^3-2079x-45198\) |
2.3.0.a.1, 6.6.0.a.1, 988.6.0.?, 2964.12.0.? |
$[(106, 962)]$ |
| 17784.p1 |
17784t1 |
17784.p |
17784t |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{10} \cdot 13^{3} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$494$ |
$2$ |
$0$ |
$0.422120753$ |
$1$ |
|
$6$ |
$9216$ |
$0.740658$ |
$-7850060032/3381183$ |
$0.84730$ |
$3.34194$ |
$[0, 0, 0, -939, 14627]$ |
\(y^2=x^3-939x+14627\) |
494.2.0.? |
$[(1, 117)]$ |
| 17784.q1 |
17784b1 |
17784.q |
17784b |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{11} \cdot 3^{9} \cdot 13^{3} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$5928$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$26496$ |
$1.034418$ |
$59007258/41743$ |
$0.82787$ |
$3.61793$ |
$[0, 0, 0, 2781, 26622]$ |
\(y^2=x^3+2781x+26622\) |
5928.2.0.? |
$[ ]$ |
| 17784.r1 |
17784g1 |
17784.r |
17784g |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{10} \cdot 3^{9} \cdot 13 \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$2964$ |
$2$ |
$0$ |
$2.785381841$ |
$1$ |
|
$2$ |
$24576$ |
$0.983325$ |
$-344700718852/6669$ |
$0.89024$ |
$4.09656$ |
$[0, 0, 0, -13251, -587122]$ |
\(y^2=x^3-13251x-587122\) |
2964.2.0.? |
$[(247, 3348)]$ |
| 17784.s1 |
17784p1 |
17784.s |
17784p |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{8} \cdot 3^{10} \cdot 13^{2} \cdot 19^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$38$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$61440$ |
$1.453127$ |
$-79891143083008/93892851$ |
$0.94140$ |
$4.51158$ |
$[0, 0, 0, -51276, -4473628]$ |
\(y^2=x^3-51276x-4473628\) |
38.2.0.a.1 |
$[ ]$ |
| 17784.t1 |
17784r1 |
17784.t |
17784r |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \) |
\( - 2^{4} \cdot 3^{8} \cdot 13 \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$494$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4608$ |
$0.101487$ |
$-256/2223$ |
$1.01345$ |
$2.50618$ |
$[0, 0, 0, -3, -245]$ |
\(y^2=x^3-3x-245\) |
494.2.0.? |
$[ ]$ |
