| 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 |
| 52371.a1 |
52371e4 |
52371.a |
52371e |
$4$ |
$4$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{9} \cdot 11^{4} \cdot 23^{6} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$6072$ |
$48$ |
$0$ |
$1.654527173$ |
$1$ |
|
$18$ |
$540672$ |
$2.104420$ |
$347873904937/395307$ |
$1.00913$ |
$4.78366$ |
$[1, -1, 1, -697586, 224210310]$ |
\(y^2+xy+y=x^3-x^2-697586x+224210310\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 88.12.0.?, 92.12.0.?, $\ldots$ |
$[(558, 2630), (29, 14268)]$ |
| 52371.a2 |
52371e2 |
52371.a |
52371e |
$4$ |
$4$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{12} \cdot 11^{2} \cdot 23^{6} \) |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$3036$ |
$48$ |
$0$ |
$6.618108692$ |
$1$ |
|
$16$ |
$270336$ |
$1.757847$ |
$169112377/88209$ |
$1.00669$ |
$4.08156$ |
$[1, -1, 1, -54851, 1566906]$ |
\(y^2+xy+y=x^3-x^2-54851x+1566906\) |
2.6.0.a.1, 12.12.0.a.1, 44.12.0.b.1, 92.12.0.?, 132.24.0.?, $\ldots$ |
$[(-4, 1338), (1199/2, 26499/2)]$ |
| 52371.a3 |
52371e1 |
52371.a |
52371e |
$4$ |
$4$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{9} \cdot 11 \cdot 23^{6} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$6072$ |
$48$ |
$0$ |
$6.618108692$ |
$1$ |
|
$11$ |
$135168$ |
$1.411274$ |
$30664297/297$ |
$1.09706$ |
$3.92443$ |
$[1, -1, 1, -31046, -2080020]$ |
\(y^2+xy+y=x^3-x^2-31046x-2080020\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 66.6.0.a.1, 88.12.0.?, $\ldots$ |
$[(-97, 156), (-100, 180)]$ |
| 52371.a4 |
52371e3 |
52371.a |
52371e |
$4$ |
$4$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( - 3^{18} \cdot 11 \cdot 23^{6} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$6072$ |
$48$ |
$0$ |
$6.618108692$ |
$1$ |
|
$8$ |
$540672$ |
$2.104420$ |
$9090072503/5845851$ |
$1.03763$ |
$4.44824$ |
$[1, -1, 1, 207004, 12041106]$ |
\(y^2+xy+y=x^3-x^2+207004x+12041106\) |
2.3.0.a.1, 4.6.0.c.1, 22.6.0.a.1, 24.12.0.ba.1, 44.12.0.g.1, $\ldots$ |
$[(374, 11715), (75, 5252)]$ |
| 52371.b1 |
52371b2 |
52371.b |
52371b |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{3} \cdot 11^{2} \cdot 23^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$3.012451107$ |
$1$ |
|
$0$ |
$98560$ |
$1.079056$ |
$19034163/121$ |
$0.94120$ |
$3.57723$ |
$[1, -1, 1, -8828, -315276]$ |
\(y^2+xy+y=x^3-x^2-8828x-315276\) |
2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.? |
$[(1066/3, 12935/3)]$ |
| 52371.b2 |
52371b1 |
52371.b |
52371b |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{3} \cdot 11 \cdot 23^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$6.024902214$ |
$1$ |
|
$3$ |
$49280$ |
$0.732483$ |
$19683/11$ |
$1.13667$ |
$2.94460$ |
$[1, -1, 1, -893, 2124]$ |
\(y^2+xy+y=x^3-x^2-893x+2124\) |
2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.? |
$[(704, 18300)]$ |
| 52371.c1 |
52371a2 |
52371.c |
52371a |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{9} \cdot 11^{2} \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$295680$ |
$1.628363$ |
$19034163/121$ |
$0.94120$ |
$4.18386$ |
$[1, -1, 0, -79449, 8591894]$ |
\(y^2+xy=x^3-x^2-79449x+8591894\) |
2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.? |
$[]$ |
| 52371.c2 |
52371a1 |
52371.c |
52371a |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{9} \cdot 11 \cdot 23^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$147840$ |
$1.281790$ |
$19683/11$ |
$1.13667$ |
$3.55122$ |
$[1, -1, 0, -8034, -49321]$ |
\(y^2+xy=x^3-x^2-8034x-49321\) |
2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.? |
$[]$ |
| 52371.d1 |
52371d6 |
52371.d |
52371d |
$6$ |
$8$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{7} \cdot 11 \cdot 23^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.89 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$64$ |
$2$ |
$0$ |
$4325376$ |
$3.232162$ |
$89254274298475942657/17457$ |
$1.00726$ |
$6.56561$ |
$[1, -1, 0, -443268243, -3591986063976]$ |
\(y^2+xy=x^3-x^2-443268243x-3591986063976\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.7, 48.48.0-48.f.1.9, 66.6.0.a.1, $\ldots$ |
$[]$ |
| 52371.d2 |
52371d4 |
52371.d |
52371d |
$6$ |
$8$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{8} \cdot 11^{2} \cdot 23^{10} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.17 |
2Cs |
$6072$ |
$192$ |
$1$ |
$1$ |
$16$ |
$2$ |
$2$ |
$2162688$ |
$2.885586$ |
$21790813729717297/304746849$ |
$0.97272$ |
$5.80014$ |
$[1, -1, 0, -27704358, -56119192065]$ |
\(y^2+xy=x^3-x^2-27704358x-56119192065\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.1, 24.48.0-24.h.1.8, 88.48.0.?, $\ldots$ |
$[]$ |
| 52371.d3 |
52371d5 |
52371.d |
52371d |
$6$ |
$8$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( - 3^{7} \cdot 11 \cdot 23^{14} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.14 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$16$ |
$2$ |
$0$ |
$4325376$ |
$3.232162$ |
$-19989223566735457/2584262514273$ |
$0.97497$ |
$5.81075$ |
$[1, -1, 0, -26918793, -59452030134]$ |
\(y^2+xy=x^3-x^2-26918793x-59452030134\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.6, 24.24.0.by.1, $\ldots$ |
$[]$ |
| 52371.d4 |
52371d3 |
52371.d |
52371d |
$6$ |
$8$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{8} \cdot 11^{8} \cdot 23^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.87 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$2162688$ |
$2.885586$ |
$309368403125137/44372288367$ |
$0.95365$ |
$5.40858$ |
$[1, -1, 0, -6708348, 5801640741]$ |
\(y^2+xy=x^3-x^2-6708348x+5801640741\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.1, 24.48.0-24.by.2.2, $\ldots$ |
$[]$ |
| 52371.d5 |
52371d2 |
52371.d |
52371d |
$6$ |
$8$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{10} \cdot 11^{4} \cdot 23^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.9 |
2Cs |
$6072$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$2$ |
$1081344$ |
$2.539013$ |
$5786435182177/627352209$ |
$0.98731$ |
$5.04239$ |
$[1, -1, 0, -1780713, -824057280]$ |
\(y^2+xy=x^3-x^2-1780713x-824057280\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.3, 12.24.0-4.b.1.2, 24.48.0-24.h.2.27, $\ldots$ |
$[]$ |
| 52371.d6 |
52371d1 |
52371.d |
52371d |
$6$ |
$8$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( - 3^{14} \cdot 11^{2} \cdot 23^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.3 |
2B |
$12144$ |
$192$ |
$1$ |
$1$ |
$4$ |
$2$ |
$1$ |
$540672$ |
$2.192440$ |
$3288008303/18259263$ |
$0.97810$ |
$4.55264$ |
$[1, -1, 0, 147492, -63958869]$ |
\(y^2+xy=x^3-x^2+147492x-63958869\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 12.12.0-4.c.1.2, 16.24.0-8.n.1.5, $\ldots$ |
$[]$ |
| 52371.e1 |
52371c2 |
52371.e |
52371c |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( 3^{11} \cdot 11^{4} \cdot 23^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$1351680$ |
$2.719540$ |
$209849322390625/1882056627$ |
$0.99362$ |
$5.37286$ |
$[1, -1, 0, -5894217, -5463595706]$ |
\(y^2+xy=x^3-x^2-5894217x-5463595706\) |
2.3.0.a.1, 12.6.0.a.1, 92.6.0.?, 276.12.0.? |
$[]$ |
| 52371.e2 |
52371c1 |
52371.e |
52371c |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( - 3^{16} \cdot 11^{2} \cdot 23^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$276$ |
$12$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$675840$ |
$2.372967$ |
$-1349232625/164333367$ |
$0.95842$ |
$4.76541$ |
$[1, -1, 0, -109602, -203066825]$ |
\(y^2+xy=x^3-x^2-109602x-203066825\) |
2.3.0.a.1, 12.6.0.b.1, 46.6.0.a.1, 276.12.0.? |
$[]$ |
| 52371.f1 |
52371f3 |
52371.f |
52371f |
$3$ |
$25$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( - 3^{6} \cdot 11 \cdot 23^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.60.0.2 |
5B.4.2 |
$37950$ |
$1200$ |
$37$ |
$1$ |
$225$ |
$3, 5$ |
$0$ |
$1897500$ |
$2.613762$ |
$-52893159101157376/11$ |
$1.09296$ |
$5.88175$ |
$[0, 0, 1, -37232607, -87444657887]$ |
\(y^2+y=x^3-37232607x-87444657887\) |
5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 110.24.1.?, 275.300.12.?, $\ldots$ |
$[]$ |
| 52371.f2 |
52371f2 |
52371.f |
52371f |
$3$ |
$25$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( - 3^{6} \cdot 11^{5} \cdot 23^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.60.0.1 |
5Cs.4.1 |
$37950$ |
$1200$ |
$37$ |
$1$ |
$9$ |
$3$ |
$0$ |
$379500$ |
$1.809044$ |
$-122023936/161051$ |
$1.01300$ |
$4.16087$ |
$[0, 0, 1, -49197, -7607417]$ |
\(y^2+y=x^3-49197x-7607417\) |
5.60.0.a.1, 22.2.0.a.1, 110.120.5.?, 275.300.12.?, 345.120.0.?, $\ldots$ |
$[]$ |
| 52371.f3 |
52371f1 |
52371.f |
52371f |
$3$ |
$25$ |
\( 3^{2} \cdot 11 \cdot 23^{2} \) |
\( - 3^{6} \cdot 11 \cdot 23^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.60.0.1 |
5B.4.1 |
$37950$ |
$1200$ |
$37$ |
$1$ |
$9$ |
$3$ |
$0$ |
$75900$ |
$1.004324$ |
$-4096/11$ |
$0.82546$ |
$3.26266$ |
$[0, 0, 1, -1587, 57793]$ |
\(y^2+y=x^3-1587x+57793\) |
5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 110.24.1.?, 275.300.12.?, $\ldots$ |
$[]$ |
