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 |
58989.a1 |
58989b1 |
58989.a |
58989b |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{2} \cdot 7 \cdot 53^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$742$ |
$2$ |
$0$ |
$1.527526160$ |
$1$ |
|
$4$ |
$943488$ |
$2.041382$ |
$-38477541376/9379251$ |
$[0, -1, 1, -197566, 40360518]$ |
\(y^2+y=x^3-x^2-197566x+40360518\) |
742.2.0.? |
$[(124, 4213)]$ |
58989.b1 |
58989f2 |
58989.b |
58989f |
$2$ |
$5$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{20} \cdot 7 \cdot 53^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$3710$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$457600$ |
$1.670849$ |
$-5770012921856/24407490807$ |
$[0, -1, 1, -19804, 3098868]$ |
\(y^2+y=x^3-x^2-19804x+3098868\) |
5.6.0.a.1, 70.12.0.a.1, 265.24.0.?, 742.2.0.?, 3710.48.1.? |
$[]$ |
58989.b2 |
58989f1 |
58989.b |
58989f |
$2$ |
$5$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{4} \cdot 7^{5} \cdot 53^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$3710$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$91520$ |
$0.866130$ |
$-1466003456/1361367$ |
$[0, -1, 1, -1254, -27178]$ |
\(y^2+y=x^3-x^2-1254x-27178\) |
5.6.0.a.1, 70.12.0.a.2, 265.24.0.?, 742.2.0.?, 3710.48.1.? |
$[]$ |
58989.c1 |
58989m1 |
58989.c |
58989m |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3^{11} \cdot 7 \cdot 53^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$0.424753134$ |
$1$ |
|
$18$ |
$52272$ |
$0.525230$ |
$2641309696/1240029$ |
$[0, 1, 1, -406, 1234]$ |
\(y^2+y=x^3+x^2-406x+1234\) |
42.2.0.a.1 |
$[(-1, 40), (-19, 49)]$ |
58989.d1 |
58989k1 |
58989.d |
58989k |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{9} \cdot 7^{5} \cdot 53^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$84$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$97200$ |
$0.993282$ |
$-364101292153/330812181$ |
$[1, 0, 0, -2099, -59514]$ |
\(y^2+xy=x^3-2099x-59514\) |
84.2.0.? |
$[]$ |
58989.e1 |
58989g2 |
58989.e |
58989g |
$2$ |
$3$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3 \cdot 7^{9} \cdot 53^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$2226$ |
$16$ |
$0$ |
$0.961303240$ |
$1$ |
|
$8$ |
$66096$ |
$0.924800$ |
$522336305152/121060821$ |
$[0, -1, 1, -2367, -33538]$ |
\(y^2+y=x^3-x^2-2367x-33538\) |
3.4.0.a.1, 42.8.0.b.1, 159.8.0.?, 2226.16.0.? |
$[(-20, 73), (176, 2229)]$ |
58989.e2 |
58989g1 |
58989.e |
58989g |
$2$ |
$3$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3^{3} \cdot 7^{3} \cdot 53^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$2226$ |
$16$ |
$0$ |
$0.961303240$ |
$1$ |
|
$8$ |
$22032$ |
$0.375494$ |
$18492424192/9261$ |
$[0, -1, 1, -777, 8597]$ |
\(y^2+y=x^3-x^2-777x+8597\) |
3.4.0.a.1, 42.8.0.b.1, 159.8.0.?, 2226.16.0.? |
$[(17, 3), (61/2, 59/2)]$ |
58989.f1 |
58989h1 |
58989.f |
58989h |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3 \cdot 7 \cdot 53^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$4.959960372$ |
$1$ |
|
$2$ |
$251856$ |
$1.711466$ |
$1736704/21$ |
$[0, -1, 1, -99251, 11941865]$ |
\(y^2+y=x^3-x^2-99251x+11941865\) |
42.2.0.a.1 |
$[(205, 410)]$ |
58989.g1 |
58989c1 |
58989.g |
58989c |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{2} \cdot 7 \cdot 53^{3} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$742$ |
$2$ |
$0$ |
$0.826052706$ |
$1$ |
|
$8$ |
$11648$ |
$0.293686$ |
$-134217728/63$ |
$[0, -1, 1, -565, 5364]$ |
\(y^2+y=x^3-x^2-565x+5364\) |
742.2.0.? |
$[(18, 26), (124, 1351)]$ |
58989.h1 |
58989n1 |
58989.h |
58989n |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{2} \cdot 7 \cdot 53^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$742$ |
$2$ |
$0$ |
$3.815956690$ |
$1$ |
|
$0$ |
$617344$ |
$2.278831$ |
$-134217728/63$ |
$[0, 1, 1, -1588021, 770034577]$ |
\(y^2+y=x^3+x^2-1588021x+770034577\) |
742.2.0.? |
$[(26209/5, 2009777/5)]$ |
58989.i1 |
58989i1 |
58989.i |
58989i |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{2} \cdot 7 \cdot 53^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$742$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$134784$ |
$1.342983$ |
$-262144/3339$ |
$[0, 1, 1, -3745, 421948]$ |
\(y^2+y=x^3+x^2-3745x+421948\) |
742.2.0.? |
$[]$ |
58989.j1 |
58989q1 |
58989.j |
58989q |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3 \cdot 7 \cdot 53^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1.747989778$ |
$1$ |
|
$2$ |
$4752$ |
$-0.273679$ |
$1736704/21$ |
$[0, 1, 1, -35, 68]$ |
\(y^2+y=x^3+x^2-35x+68\) |
42.2.0.a.1 |
$[(6, 10)]$ |
58989.k1 |
58989p1 |
58989.k |
58989p |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{2} \cdot 7^{5} \cdot 53^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$742$ |
$2$ |
$0$ |
$0.906767024$ |
$1$ |
|
$2$ |
$449280$ |
$1.998943$ |
$12747309056/8016939$ |
$[0, 1, 1, 136705, -5684818]$ |
\(y^2+y=x^3+x^2+136705x-5684818\) |
742.2.0.? |
$[(3480, 206461)]$ |
58989.l1 |
58989r2 |
58989.l |
58989r |
$2$ |
$3$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3 \cdot 7^{9} \cdot 53^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$42$ |
$16$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$3503088$ |
$2.909946$ |
$522336305152/121060821$ |
$[0, 1, 1, -6649839, -5112691201]$ |
\(y^2+y=x^3+x^2-6649839x-5112691201\) |
3.8.0-3.a.1.1, 42.16.0-42.b.1.3 |
$[]$ |
58989.l2 |
58989r1 |
58989.l |
58989r |
$2$ |
$3$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3^{3} \cdot 7^{3} \cdot 53^{8} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$42$ |
$16$ |
$0$ |
$1$ |
$4$ |
$2$ |
$2$ |
$1167696$ |
$2.360641$ |
$18492424192/9261$ |
$[0, 1, 1, -2183529, 1240634774]$ |
\(y^2+y=x^3+x^2-2183529x+1240634774\) |
3.8.0-3.a.1.2, 42.16.0-42.b.1.4 |
$[]$ |
58989.m1 |
58989d1 |
58989.m |
58989d |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{9} \cdot 7^{5} \cdot 53^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$84$ |
$2$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$5151600$ |
$2.978428$ |
$-364101292153/330812181$ |
$[1, 1, 0, -5896149, -8836681266]$ |
\(y^2+xy=x^3+x^2-5896149x-8836681266\) |
84.2.0.? |
$[]$ |
58989.n1 |
58989a6 |
58989.n |
58989a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3 \cdot 7^{2} \cdot 53^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.13 |
2B |
$17808$ |
$192$ |
$1$ |
$49.59630879$ |
$1$ |
|
$0$ |
$599040$ |
$2.059353$ |
$53297461115137/147$ |
$[1, 1, 0, -2202314, -1258878483]$ |
\(y^2+xy=x^3+x^2-2202314x-1258878483\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0.h.1, 16.24.0.e.2, $\ldots$ |
$[(172919103341329630148581/3516324812, 71182472524962197490968959493647419/3516324812)]$ |
58989.n2 |
58989a4 |
58989.n |
58989a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 53^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.18 |
2Cs |
$8904$ |
$192$ |
$1$ |
$24.79815439$ |
$1$ |
|
$2$ |
$299520$ |
$1.712778$ |
$13027640977/21609$ |
$[1, 1, 0, -137699, -19696560]$ |
\(y^2+xy=x^3+x^2-137699x-19696560\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.1, 12.24.0.c.1, 24.48.0.j.2, $\ldots$ |
$[(-935544679481/66970, 10531233706262307/66970)]$ |
58989.n3 |
58989a3 |
58989.n |
58989a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3^{8} \cdot 7 \cdot 53^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.88 |
2B |
$17808$ |
$192$ |
$1$ |
$6.199538599$ |
$1$ |
|
$0$ |
$299520$ |
$1.712778$ |
$6570725617/45927$ |
$[1, 1, 0, -109609, 13837282]$ |
\(y^2+xy=x^3+x^2-109609x+13837282\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.1, 28.12.0.h.1, 48.48.0.bf.1, $\ldots$ |
$[(38094/13, 1519250/13)]$ |
58989.n4 |
58989a5 |
58989.n |
58989a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3 \cdot 7^{8} \cdot 53^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.90 |
2B |
$17808$ |
$192$ |
$1$ |
$49.59630879$ |
$1$ |
|
$0$ |
$599040$ |
$2.059353$ |
$-4354703137/17294403$ |
$[1, 1, 0, -95564, -31924137]$ |
\(y^2+xy=x^3+x^2-95564x-31924137\) |
2.3.0.a.1, 4.6.0.c.1, 6.6.0.a.1, 8.24.0.bb.2, 12.12.0.g.1, $\ldots$ |
$[(167012913862570869323839/3459603230, 67950530295545226653745146649749077/3459603230)]$ |
58989.n5 |
58989a2 |
58989.n |
58989a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 53^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.10 |
2Cs |
$8904$ |
$192$ |
$1$ |
$12.39907719$ |
$1$ |
|
$2$ |
$149760$ |
$1.366203$ |
$7189057/3969$ |
$[1, 1, 0, -11294, -103785]$ |
\(y^2+xy=x^3+x^2-11294x-103785\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.e.2, 24.48.0.w.2, 28.24.0.c.1, $\ldots$ |
$[(-216665/74, 223621995/74)]$ |
58989.n6 |
58989a1 |
58989.n |
58989a |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{2} \cdot 7 \cdot 53^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.1 |
2B |
$17808$ |
$192$ |
$1$ |
$6.199538599$ |
$1$ |
|
$1$ |
$74880$ |
$1.019630$ |
$103823/63$ |
$[1, 1, 0, 2751, -11088]$ |
\(y^2+xy=x^3+x^2+2751x-11088\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 16.24.0.e.1, $\ldots$ |
$[(9549/28, 3296103/28)]$ |
58989.o1 |
58989j2 |
58989.o |
58989j |
$2$ |
$2$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3^{2} \cdot 7 \cdot 53^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4452$ |
$12$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$314496$ |
$1.757982$ |
$4354703137/176967$ |
$[1, 0, 1, -95565, -10972307]$ |
\(y^2+xy+y=x^3-95565x-10972307\) |
2.3.0.a.1, 28.6.0.a.1, 636.6.0.?, 4452.12.0.? |
$[]$ |
58989.o2 |
58989j1 |
58989.o |
58989j |
$2$ |
$2$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3 \cdot 7^{2} \cdot 53^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$4452$ |
$12$ |
$0$ |
$1$ |
$9$ |
$3$ |
$1$ |
$157248$ |
$1.411409$ |
$103823/7791$ |
$[1, 0, 1, 2750, -629569]$ |
\(y^2+xy+y=x^3+2750x-629569\) |
2.3.0.a.1, 28.6.0.b.1, 318.6.0.?, 4452.12.0.? |
$[]$ |
58989.p1 |
58989e1 |
58989.p |
58989e |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( 3^{11} \cdot 7 \cdot 53^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$2770416$ |
$2.510376$ |
$2641309696/1240029$ |
$[0, -1, 1, -1141390, 204290949]$ |
\(y^2+y=x^3-x^2-1141390x+204290949\) |
42.2.0.a.1 |
$[]$ |
58989.q1 |
58989l1 |
58989.q |
58989l |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{6} \cdot 7 \cdot 53^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$742$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$673920$ |
$1.716455$ |
$425259008/270459$ |
$[0, 1, 1, 44008, 1132625]$ |
\(y^2+y=x^3+x^2+44008x+1132625\) |
742.2.0.? |
$[]$ |
58989.r1 |
58989o2 |
58989.r |
58989o |
$2$ |
$5$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{20} \cdot 7 \cdot 53^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$3710$ |
$48$ |
$1$ |
$5.991936654$ |
$1$ |
|
$0$ |
$24252800$ |
$3.655994$ |
$-5770012921856/24407490807$ |
$[0, 1, 1, -55630372, 460348867267]$ |
\(y^2+y=x^3+x^2-55630372x+460348867267\) |
5.6.0.a.1, 70.12.0.a.1, 265.24.0.?, 742.2.0.?, 3710.48.1.? |
$[(422285/2, 273784799/2)]$ |
58989.r2 |
58989o1 |
58989.r |
58989o |
$2$ |
$5$ |
\( 3 \cdot 7 \cdot 53^{2} \) |
\( - 3^{4} \cdot 7^{5} \cdot 53^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.6.0.1 |
5B |
$3710$ |
$48$ |
$1$ |
$29.95968327$ |
$1$ |
|
$0$ |
$4850560$ |
$2.851276$ |
$-1466003456/1361367$ |
$[0, 1, 1, -3523422, -4109557975]$ |
\(y^2+y=x^3+x^2-3523422x-4109557975\) |
5.6.0.a.1, 70.12.0.a.2, 265.24.0.?, 742.2.0.?, 3710.48.1.? |
$[(7093838066233869/1266698, 525104948677443568542863/1266698)]$ |