| 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 |
| 427119.a1 |
427119a1 |
427119.a |
427119a |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{7} \cdot 7 \cdot 11^{4} \cdot 43^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1542912$ |
$1.192898$ |
$560617204830208/224139069$ |
$0.92865$ |
$3.19962$ |
$[0, -1, 1, -21084, -1170952]$ |
\(y^2+y=x^3-x^2-21084x-1170952\) |
42.2.0.a.1 |
$[]$ |
| 427119.b1 |
427119b1 |
427119.b |
427119b |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3 \cdot 7 \cdot 11^{2} \cdot 43^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$18840192$ |
$2.490170$ |
$7573504/2541$ |
$0.76329$ |
$4.12286$ |
$[0, 1, 1, -1139600, -303925078]$ |
\(y^2+y=x^3+x^2-1139600x-303925078\) |
42.2.0.a.1 |
$[]$ |
| 427119.c1 |
427119c2 |
427119.c |
427119c |
$2$ |
$2$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{4} \cdot 7 \cdot 11^{6} \cdot 43^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$13244$ |
$12$ |
$0$ |
$20.17991863$ |
$1$ |
|
$0$ |
$54489600$ |
$3.247295$ |
$2611538513011/1004475087$ |
$0.91358$ |
$4.81625$ |
$[1, 1, 1, -22810227, 24273261876]$ |
\(y^2+xy+y=x^3+x^2-22810227x+24273261876\) |
2.3.0.a.1, 308.6.0.?, 602.6.0.?, 1892.6.0.?, 13244.12.0.? |
$[(447780217/632, 2530243555759/632)]$ |
| 427119.c2 |
427119c1 |
427119.c |
427119c |
$2$ |
$2$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{2} \cdot 7^{2} \cdot 11^{3} \cdot 43^{9} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$13244$ |
$12$ |
$0$ |
$10.08995931$ |
$1$ |
|
$1$ |
$27244800$ |
$2.900723$ |
$1767610869571/586971$ |
$0.89479$ |
$4.78614$ |
$[1, 1, 1, -20027482, 34479257438]$ |
\(y^2+xy+y=x^3+x^2-20027482x+34479257438\) |
2.3.0.a.1, 308.6.0.?, 946.6.0.?, 1204.6.0.?, 13244.12.0.? |
$[(123929/8, 27376887/8)]$ |
| 427119.d1 |
427119d1 |
427119.d |
427119d |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( - 3^{25} \cdot 7 \cdot 11^{3} \cdot 43^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$39732$ |
$2$ |
$0$ |
$38.77352876$ |
$1$ |
|
$0$ |
$16948800$ |
$2.678001$ |
$-2865339168402418219/7894187974180431$ |
$0.99870$ |
$4.28343$ |
$[1, 1, 1, -1272387, -1326447306]$ |
\(y^2+xy+y=x^3+x^2-1272387x-1326447306\) |
39732.2.0.? |
$[(414027540021939884/7016719, 262265621101489594333459914/7016719)]$ |
| 427119.e1 |
427119e2 |
427119.e |
427119e |
$2$ |
$2$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 11^{2} \cdot 43^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1204$ |
$12$ |
$0$ |
$8.796262409$ |
$1$ |
|
$0$ |
$23654400$ |
$2.868576$ |
$2362760750223042625/20650707$ |
$0.93698$ |
$5.00382$ |
$[1, 1, 0, -51306090, 141428147949]$ |
\(y^2+xy=x^3+x^2-51306090x+141428147949\) |
2.3.0.a.1, 28.6.0.c.1, 172.6.0.?, 1204.12.0.? |
$[(1066065/16, 4841727/16)]$ |
| 427119.e2 |
427119e1 |
427119.e |
427119e |
$2$ |
$2$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( - 3^{2} \cdot 7 \cdot 11^{4} \cdot 43^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1204$ |
$12$ |
$0$ |
$4.398131204$ |
$1$ |
|
$3$ |
$11827200$ |
$2.522003$ |
$-575618923356625/1705486167$ |
$0.88933$ |
$4.36248$ |
$[1, 1, 0, -3204355, 2212106512]$ |
\(y^2+xy=x^3+x^2-3204355x+2212106512\) |
2.3.0.a.1, 14.6.0.b.1, 172.6.0.?, 1204.12.0.? |
$[(748, 14938)]$ |
| 427119.f1 |
427119f4 |
427119.f |
427119f |
$4$ |
$4$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{4} \cdot 7 \cdot 11^{8} \cdot 43^{7} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$2408$ |
$48$ |
$0$ |
$128.0668238$ |
$1$ |
|
$0$ |
$75694080$ |
$3.438210$ |
$244865207835604217233/5226283877661$ |
$0.95773$ |
$5.36178$ |
$[1, 0, 1, -240993152, -1439969234515]$ |
\(y^2+xy+y=x^3-240993152x-1439969234515\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 56.24.0-56.z.1.5, 344.24.0.?, 602.6.0.?, $\ldots$ |
$[(82359/2, 12121037/2), (22484765241/680, 3165146857474049/680)]$ |
| 427119.f2 |
427119f3 |
427119.f |
427119f |
$4$ |
$4$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{16} \cdot 7^{4} \cdot 11^{2} \cdot 43^{7} \) |
$2$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$2408$ |
$48$ |
$0$ |
$8.004176493$ |
$1$ |
|
$10$ |
$75694080$ |
$3.438210$ |
$4520419245516634993/537756986560563$ |
$0.94246$ |
$5.05386$ |
$[1, 0, 1, -63692542, 174380010929]$ |
\(y^2+xy+y=x^3-63692542x+174380010929\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 56.24.0-56.z.1.13, 172.24.0.?, 2408.48.0.? |
$[(2821, 129566), (19453, 2499626)]$ |
| 427119.f3 |
427119f2 |
427119.f |
427119f |
$4$ |
$4$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{8} \cdot 7^{2} \cdot 11^{4} \cdot 43^{8} \) |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$1204$ |
$48$ |
$0$ |
$32.01670597$ |
$1$ |
|
$6$ |
$37847040$ |
$3.091633$ |
$66300793297143553/8703095910201$ |
$0.92121$ |
$4.72819$ |
$[1, 0, 1, -15590807, -20836070395]$ |
\(y^2+xy+y=x^3-15590807x-20836070395\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 28.24.0-28.b.1.3, 172.24.0.?, 1204.48.0.? |
$[(-2415, 53479), (-977739/19, 277094251/19)]$ |
| 427119.f4 |
427119f1 |
427119.f |
427119f |
$4$ |
$4$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( - 3^{4} \cdot 7 \cdot 11^{2} \cdot 43^{10} \) |
$2$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$2408$ |
$48$ |
$0$ |
$32.01670597$ |
$1$ |
|
$3$ |
$18923520$ |
$2.745060$ |
$59424010905167/234553680207$ |
$0.90401$ |
$4.32280$ |
$[1, 0, 1, 1503198, -1711297601]$ |
\(y^2+xy+y=x^3+1503198x-1711297601\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 14.6.0.b.1, 28.12.0.g.1, $\ldots$ |
$[(68219/7, 18798366/7), (1823, 83280)]$ |
| 427119.g1 |
427119g2 |
427119.g |
427119g |
$2$ |
$2$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{4} \cdot 7 \cdot 11^{6} \cdot 43^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$13244$ |
$12$ |
$0$ |
$3.985261309$ |
$1$ |
|
$2$ |
$1267200$ |
$1.366695$ |
$2611538513011/1004475087$ |
$0.91358$ |
$3.07560$ |
$[1, 0, 1, -12337, -306445]$ |
\(y^2+xy+y=x^3-12337x-306445\) |
2.3.0.a.1, 308.6.0.?, 602.6.0.?, 1892.6.0.?, 13244.12.0.? |
$[(-95, -55)]$ |
| 427119.g2 |
427119g1 |
427119.g |
427119g |
$2$ |
$2$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{2} \cdot 7^{2} \cdot 11^{3} \cdot 43^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$13244$ |
$12$ |
$0$ |
$7.970522619$ |
$1$ |
|
$1$ |
$633600$ |
$1.020123$ |
$1767610869571/586971$ |
$0.89479$ |
$3.04549$ |
$[1, 0, 1, -10832, -434671]$ |
\(y^2+xy+y=x^3-10832x-434671\) |
2.3.0.a.1, 308.6.0.?, 946.6.0.?, 1204.6.0.?, 13244.12.0.? |
$[(86013/4, 25049635/4)]$ |
| 427119.h1 |
427119h1 |
427119.h |
427119h |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( - 3^{25} \cdot 7 \cdot 11^{3} \cdot 43^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$39732$ |
$2$ |
$0$ |
$9.518731126$ |
$1$ |
|
$0$ |
$728798400$ |
$4.558601$ |
$-2865339168402418219/7894187974180431$ |
$0.99870$ |
$6.02408$ |
$[1, 0, 1, -2352643602, 105419498359189]$ |
\(y^2+xy+y=x^3-2352643602x+105419498359189\) |
39732.2.0.? |
$[(26102477/11, 130517523948/11)]$ |
| 427119.i1 |
427119i5 |
427119.i |
427119i |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{8} \cdot 7 \cdot 11^{2} \cdot 43^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.5 |
2B |
$158928$ |
$192$ |
$1$ |
$6.451666877$ |
$1$ |
|
$0$ |
$12902400$ |
$2.503391$ |
$10206027697760497/5557167$ |
$1.00022$ |
$4.58386$ |
$[1, 0, 1, -8355670, 9295810493]$ |
\(y^2+xy+y=x^3-8355670x+9295810493\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 28.12.0.h.1, 48.24.0.e.2, $\ldots$ |
$[(-152543/7, 25123580/7)]$ |
| 427119.i2 |
427119i3 |
427119.i |
427119i |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{4} \cdot 7^{2} \cdot 11^{4} \cdot 43^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.3 |
2Cs |
$79464$ |
$192$ |
$1$ |
$12.90333375$ |
$1$ |
|
$2$ |
$6451200$ |
$2.156815$ |
$2533811507137/58110129$ |
$0.95470$ |
$3.94359$ |
$[1, 0, 1, -525155, 143504561]$ |
\(y^2+xy+y=x^3-525155x+143504561\) |
2.6.0.a.1, 4.12.0.b.1, 24.24.0.i.1, 28.24.0.c.1, 88.24.0.?, $\ldots$ |
$[(-6449511/91, 7043300545/91)]$ |
| 427119.i3 |
427119i2 |
427119.i |
427119i |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{2} \cdot 7^{4} \cdot 11^{2} \cdot 43^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.3 |
2Cs |
$79464$ |
$192$ |
$1$ |
$25.80666750$ |
$1$ |
|
$2$ |
$3225600$ |
$1.810244$ |
$6570725617/2614689$ |
$0.92677$ |
$3.48428$ |
$[1, 0, 1, -72150, -4175069]$ |
\(y^2+xy+y=x^3-72150x-4175069\) |
2.6.0.a.1, 4.12.0.b.1, 24.24.0.i.2, 56.24.0.m.1, 88.24.0.?, $\ldots$ |
$[(-206948989537/30667, 32828833801768068/30667)]$ |
| 427119.i4 |
427119i1 |
427119.i |
427119i |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3 \cdot 7^{2} \cdot 11 \cdot 43^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.5 |
2B |
$158928$ |
$192$ |
$1$ |
$51.61333501$ |
$1$ |
|
$1$ |
$1612800$ |
$1.463669$ |
$4354703137/1617$ |
$0.90109$ |
$3.45255$ |
$[1, 0, 1, -62905, -6075841]$ |
\(y^2+xy+y=x^3-62905x-6075841\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 48.24.0.e.1, 66.6.0.a.1, $\ldots$ |
$[(-88463477217456279239003/24615511557, 520990279457592571904420065725109/24615511557)]$ |
| 427119.i5 |
427119i6 |
427119.i |
427119i |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( - 3^{2} \cdot 7 \cdot 11^{8} \cdot 43^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.5 |
2B |
$158928$ |
$192$ |
$1$ |
$25.80666750$ |
$1$ |
|
$0$ |
$12902400$ |
$2.503391$ |
$3288008303/13504609503$ |
$1.06765$ |
$4.11483$ |
$[1, 0, 1, 57280, 444506969]$ |
\(y^2+xy+y=x^3+57280x+444506969\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 14.6.0.b.1, 24.24.0.bz.2, $\ldots$ |
$[(11806003948923/20894, 40444161423171027317/20894)]$ |
| 427119.i6 |
427119i4 |
427119.i |
427119i |
$6$ |
$8$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( - 3 \cdot 7^{8} \cdot 11 \cdot 43^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.5 |
2B |
$158928$ |
$192$ |
$1$ |
$51.61333501$ |
$1$ |
|
$0$ |
$6451200$ |
$2.156815$ |
$221115865823/190238433$ |
$0.96278$ |
$3.75548$ |
$[1, 0, 1, 232935, -30168311]$ |
\(y^2+xy+y=x^3+232935x-30168311\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 24.24.0.bz.1, 88.24.0.?, $\ldots$ |
$[(7670800737326028418687/6847757098, 1100678058090079400265090356880701/6847757098)]$ |
| 427119.j1 |
427119j1 |
427119.j |
427119j |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3 \cdot 7 \cdot 11^{2} \cdot 43^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1.354815903$ |
$1$ |
|
$0$ |
$438144$ |
$0.609570$ |
$7573504/2541$ |
$0.76329$ |
$2.38221$ |
$[0, -1, 1, -616, 4023]$ |
\(y^2+y=x^3-x^2-616x+4023\) |
42.2.0.a.1 |
$[(-99/2, 469/2)]$ |
| 427119.k1 |
427119k1 |
427119.k |
427119k |
$1$ |
$1$ |
\( 3 \cdot 7 \cdot 11 \cdot 43^{2} \) |
\( 3^{7} \cdot 7 \cdot 11^{4} \cdot 43^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$42$ |
$2$ |
$0$ |
$1.162079894$ |
$1$ |
|
$0$ |
$66345216$ |
$3.073498$ |
$560617204830208/224139069$ |
$0.92865$ |
$4.94027$ |
$[0, 1, 1, -38984932, 93644646895]$ |
\(y^2+y=x^3+x^2-38984932x+93644646895\) |
42.2.0.a.1 |
$[(56081/4, 549121/4)]$ |
