| 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 |
| 37845.a1 |
37845a1 |
37845.a |
37845a |
$1$ |
$1$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{9} \cdot 5 \cdot 29^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$870$ |
$2$ |
$0$ |
$1.167693465$ |
$1$ |
|
$2$ |
$201600$ |
$1.608206$ |
$110592/145$ |
$0.73528$ |
$3.97870$ |
$[0, 0, 1, 22707, -1481632]$ |
\(y^2+y=x^3+22707x-1481632\) |
870.2.0.? |
$[(1044, 34060)]$ |
| 37845.b1 |
37845f1 |
37845.b |
37845f |
$1$ |
$1$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{7} \cdot 5^{2} \cdot 29^{2} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.441201069$ |
$1$ |
|
$16$ |
$14400$ |
$0.159336$ |
$118784/75$ |
$0.81570$ |
$2.37271$ |
$[0, 0, 1, 87, 94]$ |
\(y^2+y=x^3+87x+94\) |
6.2.0.a.1 |
$[(4, 22), (-1, 2)]$ |
| 37845.c1 |
37845e4 |
37845.c |
37845e |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{8} \cdot 5 \cdot 29^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.10 |
2B |
$6960$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$2150400$ |
$2.777073$ |
$37286818682653441/1305$ |
$1.23338$ |
$6.16178$ |
$[1, -1, 1, -52680398, 147183980316]$ |
\(y^2+xy+y=x^3-x^2-52680398x+147183980316\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 48.24.0.j.1, 60.12.0-4.c.1.1, $\ldots$ |
$[]$ |
| 37845.c2 |
37845e2 |
37845.c |
37845e |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{10} \cdot 5^{2} \cdot 29^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.4 |
2Cs |
$3480$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$1075200$ |
$2.430500$ |
$9104453457841/1703025$ |
$1.03605$ |
$5.37272$ |
$[1, -1, 1, -3292673, 2300150256]$ |
\(y^2+xy+y=x^3-x^2-3292673x+2300150256\) |
2.6.0.a.1, 4.12.0.a.1, 24.24.0.j.1, 40.24.0-4.a.1.5, 60.24.0-4.a.1.2, $\ldots$ |
$[]$ |
| 37845.c3 |
37845e3 |
37845.c |
37845e |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{8} \cdot 5^{4} \cdot 29^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.9 |
2B |
$6960$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$2150400$ |
$2.777073$ |
$-6561258219361/3978455625$ |
$0.95298$ |
$5.40964$ |
$[1, -1, 1, -2952068, 2794436232]$ |
\(y^2+xy+y=x^3-x^2-2952068x+2794436232\) |
2.3.0.a.1, 4.12.0.d.1, 24.24.0.z.1, 40.24.0-4.d.1.5, 120.48.0.?, $\ldots$ |
$[]$ |
| 37845.c4 |
37845e1 |
37845.c |
37845e |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{14} \cdot 5 \cdot 29^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.10 |
2B |
$6960$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$537600$ |
$2.083927$ |
$2992209121/951345$ |
$0.88867$ |
$4.61185$ |
$[1, -1, 1, -227228, 28042422]$ |
\(y^2+xy+y=x^3-x^2-227228x+28042422\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 48.24.0.j.1, 60.12.0-4.c.1.2, $\ldots$ |
$[]$ |
| 37845.d1 |
37845d8 |
37845.d |
37845d |
$8$ |
$16$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{10} \cdot 5 \cdot 29^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.121 |
2B |
$13920$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$802816$ |
$2.523823$ |
$1114544804970241/405$ |
$1.07354$ |
$5.82878$ |
$[1, -1, 1, -16349198, 25448520512]$ |
\(y^2+xy+y=x^3-x^2-16349198x+25448520512\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.bb.2, 10.6.0.a.1, 16.48.0.x.2, $\ldots$ |
$[]$ |
| 37845.d2 |
37845d6 |
37845.d |
37845d |
$8$ |
$16$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{14} \cdot 5^{2} \cdot 29^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.123 |
2Cs |
$6960$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$401408$ |
$2.177250$ |
$272223782641/164025$ |
$1.03897$ |
$5.03976$ |
$[1, -1, 1, -1021973, 397703972]$ |
\(y^2+xy+y=x^3-x^2-1021973x+397703972\) |
2.6.0.a.1, 4.12.0.b.1, 8.48.0.k.1, 20.24.0.c.1, 40.96.1.cc.2, $\ldots$ |
$[]$ |
| 37845.d3 |
37845d7 |
37845.d |
37845d |
$8$ |
$16$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{22} \cdot 5 \cdot 29^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.134 |
2B |
$13920$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$802816$ |
$2.523823$ |
$-147281603041/215233605$ |
$1.05949$ |
$5.10101$ |
$[1, -1, 1, -832748, 549386732]$ |
\(y^2+xy+y=x^3-x^2-832748x+549386732\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0.ba.2, 16.48.0.u.2, 20.12.0.h.1, $\ldots$ |
$[]$ |
| 37845.d4 |
37845d4 |
37845.d |
37845d |
$8$ |
$16$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{7} \cdot 5 \cdot 29^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.48.0.1 |
2B |
$13920$ |
$768$ |
$13$ |
$1$ |
$4$ |
$2$ |
$0$ |
$200704$ |
$1.830677$ |
$56667352321/15$ |
$1.03019$ |
$4.89087$ |
$[1, -1, 1, -605678, -181279114]$ |
\(y^2+xy+y=x^3-x^2-605678x-181279114\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.by.2, $\ldots$ |
$[]$ |
| 37845.d5 |
37845d3 |
37845.d |
37845d |
$8$ |
$16$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{10} \cdot 5^{4} \cdot 29^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.44 |
2Cs |
$6960$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$200704$ |
$1.830677$ |
$111284641/50625$ |
$1.02534$ |
$4.29959$ |
$[1, -1, 1, -75848, 3737522]$ |
\(y^2+xy+y=x^3-x^2-75848x+3737522\) |
2.6.0.a.1, 4.24.0.b.1, 8.48.0.b.2, 24.96.1.n.1, 40.96.1.s.1, $\ldots$ |
$[]$ |
| 37845.d6 |
37845d2 |
37845.d |
37845d |
$8$ |
$16$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 29^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.3 |
2Cs |
$6960$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$100352$ |
$1.484102$ |
$13997521/225$ |
$0.96230$ |
$4.10291$ |
$[1, -1, 1, -38003, -2802094]$ |
\(y^2+xy+y=x^3-x^2-38003x-2802094\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0.i.1, 16.48.0.d.2, 24.48.0.bb.2, $\ldots$ |
$[]$ |
| 37845.d7 |
37845d1 |
37845.d |
37845d |
$8$ |
$16$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{7} \cdot 5 \cdot 29^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.48.0.1 |
2B |
$13920$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$1$ |
$50176$ |
$1.137529$ |
$-1/15$ |
$1.19808$ |
$3.50606$ |
$[1, -1, 1, -158, -122668]$ |
\(y^2+xy+y=x^3-x^2-158x-122668\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0.g.1, 24.24.0.bz.1, $\ldots$ |
$[]$ |
| 37845.d8 |
37845d5 |
37845.d |
37845d |
$8$ |
$16$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{8} \cdot 5^{8} \cdot 29^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.197 |
2B |
$13920$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$401408$ |
$2.177250$ |
$4733169839/3515625$ |
$1.05585$ |
$4.65536$ |
$[1, -1, 1, 264757, 27852356]$ |
\(y^2+xy+y=x^3-x^2+264757x+27852356\) |
2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 24.96.1.cv.2, 80.96.1.?, $\ldots$ |
$[]$ |
| 37845.e1 |
37845j1 |
37845.e |
37845j |
$2$ |
$2$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{6} \cdot 5 \cdot 29^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.3 |
2B |
$3480$ |
$48$ |
$0$ |
$1.658476194$ |
$1$ |
|
$3$ |
$107520$ |
$1.396452$ |
$2146689/145$ |
$0.84440$ |
$3.92504$ |
$[1, -1, 1, -20342, -1044404]$ |
\(y^2+xy+y=x^3-x^2-20342x-1044404\) |
2.3.0.a.1, 4.6.0.b.1, 120.12.0.?, 290.6.0.?, 580.24.0.?, $\ldots$ |
$[(979, 29786)]$ |
| 37845.e2 |
37845j2 |
37845.e |
37845j |
$2$ |
$2$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{6} \cdot 5^{2} \cdot 29^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.5 |
2B |
$3480$ |
$48$ |
$0$ |
$3.316952389$ |
$1$ |
|
$0$ |
$215040$ |
$1.743027$ |
$1367631/21025$ |
$0.96200$ |
$4.18975$ |
$[1, -1, 1, 17503, -4511006]$ |
\(y^2+xy+y=x^3-x^2+17503x-4511006\) |
2.3.0.a.1, 4.6.0.a.1, 120.12.0.?, 580.12.0.?, 696.12.0.?, $\ldots$ |
$[(3887/2, 239999/2)]$ |
| 37845.f1 |
37845i1 |
37845.f |
37845i |
$1$ |
$1$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{11} \cdot 5^{7} \cdot 29^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$870$ |
$2$ |
$0$ |
$0.738347201$ |
$1$ |
|
$4$ |
$940800$ |
$2.591248$ |
$53838872576/550546875$ |
$1.03969$ |
$5.15293$ |
$[0, 0, 1, 595428, 722042442]$ |
\(y^2+y=x^3+595428x+722042442\) |
870.2.0.? |
$[(6032, 473062)]$ |
| 37845.g1 |
37845h1 |
37845.g |
37845h |
$2$ |
$3$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{9} \cdot 5 \cdot 29^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$870$ |
$16$ |
$0$ |
$5.245176868$ |
$1$ |
|
$0$ |
$134400$ |
$1.707781$ |
$-160989184/3915$ |
$0.86981$ |
$4.33852$ |
$[0, 0, 1, -85782, -9871448]$ |
\(y^2+y=x^3-85782x-9871448\) |
3.4.0.a.1, 30.8.0-3.a.1.1, 87.8.0.?, 870.16.0.? |
$[(29290/7, 4234684/7)]$ |
| 37845.g2 |
37845h2 |
37845.g |
37845h |
$2$ |
$3$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{7} \cdot 5^{3} \cdot 29^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$870$ |
$16$ |
$0$ |
$1.748392289$ |
$1$ |
|
$4$ |
$403200$ |
$2.257088$ |
$12747309056/9145875$ |
$0.97110$ |
$4.74934$ |
$[0, 0, 1, 368358, -42138095]$ |
\(y^2+y=x^3+368358x-42138095\) |
3.4.0.a.1, 30.8.0-3.a.1.2, 87.8.0.?, 870.16.0.? |
$[(145, 3784)]$ |
| 37845.h1 |
37845c4 |
37845.h |
37845c |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{8} \cdot 5 \cdot 29^{10} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3480$ |
$48$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$1290240$ |
$2.470604$ |
$1888690601881/31827645$ |
$0.93261$ |
$5.22351$ |
$[1, -1, 0, -1949175, 1032552796]$ |
\(y^2+xy=x^3-x^2-1949175x+1032552796\) |
2.3.0.a.1, 4.6.0.c.1, 10.6.0.a.1, 20.12.0.g.1, 24.12.0-4.c.1.3, $\ldots$ |
$[]$ |
| 37845.h2 |
37845c2 |
37845.h |
37845c |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{10} \cdot 5^{2} \cdot 29^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$1740$ |
$48$ |
$0$ |
$1$ |
$9$ |
$3$ |
$2$ |
$645120$ |
$2.124031$ |
$3803721481/1703025$ |
$0.90376$ |
$4.63462$ |
$[1, -1, 0, -246150, -22300889]$ |
\(y^2+xy=x^3-x^2-246150x-22300889\) |
2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.b.1, 60.24.0-20.b.1.3, 116.12.0.?, $\ldots$ |
$[]$ |
| 37845.h3 |
37845c1 |
37845.h |
37845c |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( 3^{8} \cdot 5 \cdot 29^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3480$ |
$48$ |
$0$ |
$1$ |
$9$ |
$3$ |
$1$ |
$322560$ |
$1.777458$ |
$2305199161/1305$ |
$0.87163$ |
$4.58711$ |
$[1, -1, 0, -208305, -36523040]$ |
\(y^2+xy=x^3-x^2-208305x-36523040\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 40.12.0.z.1, 120.24.0.?, $\ldots$ |
$[]$ |
| 37845.h4 |
37845c3 |
37845.h |
37845c |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{14} \cdot 5^{4} \cdot 29^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$3480$ |
$48$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$1290240$ |
$2.470604$ |
$157376536199/118918125$ |
$0.94171$ |
$4.98777$ |
$[1, -1, 0, 851355, -167391050]$ |
\(y^2+xy=x^3-x^2+851355x-167391050\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 40.12.0.z.1, 116.12.0.?, $\ldots$ |
$[]$ |
| 37845.i1 |
37845g1 |
37845.i |
37845g |
$1$ |
$1$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{7} \cdot 5^{2} \cdot 29^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$3.985731744$ |
$1$ |
|
$0$ |
$417600$ |
$1.842983$ |
$118784/75$ |
$0.81570$ |
$4.28935$ |
$[0, 0, 1, 73167, 2298663]$ |
\(y^2+y=x^3+73167x+2298663\) |
6.2.0.a.1 |
$[(841/6, 433007/6)]$ |
| 37845.j1 |
37845b1 |
37845.j |
37845b |
$1$ |
$1$ |
\( 3^{2} \cdot 5 \cdot 29^{2} \) |
\( - 3^{3} \cdot 5 \cdot 29^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$870$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$67200$ |
$1.058899$ |
$110592/145$ |
$0.73528$ |
$3.35338$ |
$[0, 0, 1, 2523, 54875]$ |
\(y^2+y=x^3+2523x+54875\) |
870.2.0.? |
$[]$ |
