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 |
1848.a1 |
1848c1 |
1848.a |
1848c |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{4} \cdot 3 \cdot 7 \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$462$ |
$2$ |
$0$ |
$0.252492919$ |
$1$ |
|
$6$ |
$160$ |
$-0.518612$ |
$-12967168/231$ |
$0.77180$ |
$2.55001$ |
$[0, -1, 0, -12, 21]$ |
\(y^2=x^3-x^2-12x+21\) |
462.2.0.? |
$[(2, 1)]$ |
1848.b1 |
1848a1 |
1848.b |
1848a |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{4} \cdot 3^{3} \cdot 7 \cdot 11^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$462$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.140484$ |
$-91238612224/251559$ |
$0.90714$ |
$3.72436$ |
$[0, -1, 0, -236, -1323]$ |
\(y^2=x^3-x^2-236x-1323\) |
462.2.0.? |
$[ ]$ |
1848.c1 |
1848h2 |
1848.c |
1848h |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{11} \cdot 3^{4} \cdot 7^{2} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$2.508793443$ |
$1$ |
|
$3$ |
$768$ |
$0.348568$ |
$4866277250/43659$ |
$0.89537$ |
$3.97910$ |
$[0, -1, 0, -448, -3476]$ |
\(y^2=x^3-x^2-448x-3476\) |
2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.? |
$[(25, 18)]$ |
1848.c2 |
1848h1 |
1848.c |
1848h |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{10} \cdot 3^{2} \cdot 7 \cdot 11^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1.254396721$ |
$1$ |
|
$7$ |
$384$ |
$0.001994$ |
$-62500/7623$ |
$0.98433$ |
$3.10161$ |
$[0, -1, 0, -8, -132]$ |
\(y^2=x^3-x^2-8x-132\) |
2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.? |
$[(14, 48)]$ |
1848.d1 |
1848b3 |
1848.d |
1848b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{11} \cdot 3^{12} \cdot 7^{8} \cdot 11^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$264$ |
$48$ |
$0$ |
$1.374838482$ |
$1$ |
|
$3$ |
$46080$ |
$2.337139$ |
$14171198121996897746/4077720290568771$ |
$1.03437$ |
$6.87627$ |
$[0, -1, 0, -640232, -139597332]$ |
\(y^2=x^3-x^2-640232x-139597332\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 24.24.0-24.bb.1.16, 44.12.0-4.c.1.1, $\ldots$ |
$[(-479, 7546)]$ |
1848.d2 |
1848b2 |
1848.d |
1848b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{10} \cdot 3^{6} \cdot 7^{4} \cdot 11^{6} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$264$ |
$48$ |
$0$ |
$2.749676965$ |
$1$ |
|
$7$ |
$23040$ |
$1.990564$ |
$21843440425782779332/3100814593569$ |
$1.02507$ |
$6.84165$ |
$[0, -1, 0, -586992, -172882980]$ |
\(y^2=x^3-x^2-586992x-172882980\) |
2.6.0.a.1, 8.12.0-2.a.1.1, 12.12.0-2.a.1.1, 24.24.0-24.a.1.3, 44.12.0-2.a.1.1, $\ldots$ |
$[(962, 12320)]$ |
1848.d3 |
1848b1 |
1848.d |
1848b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{8} \cdot 3^{3} \cdot 7^{2} \cdot 11^{3} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.12 |
2B |
$264$ |
$48$ |
$0$ |
$5.499353930$ |
$1$ |
|
$3$ |
$11520$ |
$1.643991$ |
$87364831012240243408/1760913$ |
$1.02507$ |
$6.84163$ |
$[0, -1, 0, -586972, -172895372]$ |
\(y^2=x^3-x^2-586972x-172895372\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.2, 12.12.0-4.c.1.2, 24.24.0-24.bb.1.2, $\ldots$ |
$[(5958, 455840)]$ |
1848.d4 |
1848b4 |
1848.d |
1848b |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{11} \cdot 3^{3} \cdot 7^{2} \cdot 11^{12} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$264$ |
$48$ |
$0$ |
$5.499353930$ |
$1$ |
|
$1$ |
$46080$ |
$2.337139$ |
$-8226100326647904626/4152140742401883$ |
$1.03134$ |
$6.88734$ |
$[0, -1, 0, -534072, -205375860]$ |
\(y^2=x^3-x^2-534072x-205375860\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 12.12.0-4.c.1.1, 24.24.0-24.v.1.4, $\ldots$ |
$[(23861/5, 1548316/5)]$ |
1848.e1 |
1848e2 |
1848.e |
1848e |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{11} \cdot 3^{8} \cdot 7^{2} \cdot 11^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$7680$ |
$1.369789$ |
$9791533777258802/427901859$ |
$0.99685$ |
$5.90877$ |
$[0, 1, 0, -56600, -5201616]$ |
\(y^2=x^3+x^2-56600x-5201616\) |
2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.? |
$[ ]$ |
1848.e2 |
1848e1 |
1848.e |
1848e |
$2$ |
$2$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{10} \cdot 3^{4} \cdot 7 \cdot 11^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$3840$ |
$1.023216$ |
$-4097989445764/1004475087$ |
$0.95402$ |
$4.82941$ |
$[0, 1, 0, -3360, -90576]$ |
\(y^2=x^3+x^2-3360x-90576\) |
2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.? |
$[ ]$ |
1848.f1 |
1848l1 |
1848.f |
1848l |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{4} \cdot 3^{7} \cdot 7^{3} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$462$ |
$2$ |
$0$ |
$0.048426699$ |
$1$ |
|
$12$ |
$672$ |
$0.237277$ |
$-12967168/8251551$ |
$0.99302$ |
$3.47708$ |
$[0, 1, 0, -12, 549]$ |
\(y^2=x^3+x^2-12x+549\) |
462.2.0.? |
$[(-6, 21)]$ |
1848.g1 |
1848j5 |
1848.g |
1848j |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{11} \cdot 3^{2} \cdot 7^{8} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.173 |
2B |
$1232$ |
$192$ |
$1$ |
$4.720509114$ |
$1$ |
|
$1$ |
$6144$ |
$1.430304$ |
$5701568801608514/6277868289$ |
$0.99431$ |
$5.83687$ |
$[0, 1, 0, -47264, -3967008]$ |
\(y^2=x^3+x^2-47264x-3967008\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.r.1.6, 88.96.0.?, 112.96.0.?, $\ldots$ |
$[(-491/2, 105/2)]$ |
1848.g2 |
1848j3 |
1848.g |
1848j |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{10} \cdot 3^{4} \cdot 7^{4} \cdot 11^{4} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.30 |
2Cs |
$616$ |
$192$ |
$1$ |
$2.360254557$ |
$1$ |
|
$7$ |
$3072$ |
$1.083731$ |
$5489767279588/2847396321$ |
$0.98782$ |
$4.82133$ |
$[0, 1, 0, -3704, -29184]$ |
\(y^2=x^3+x^2-3704x-29184\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.48.0-8.c.1.2, 56.96.0-56.e.2.1, 88.96.0.?, $\ldots$ |
$[(-32, 240)]$ |
1848.g3 |
1848j2 |
1848.g |
1848j |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.29 |
2Cs |
$616$ |
$192$ |
$1$ |
$1.180127278$ |
$1$ |
|
$21$ |
$1536$ |
$0.737157$ |
$3911877700432/38900169$ |
$1.03181$ |
$4.59198$ |
$[0, 1, 0, -2084, 35616]$ |
\(y^2=x^3+x^2-2084x+35616\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.48.0-8.h.1.9, 56.96.0-56.x.2.5, 88.96.0.?, $\ldots$ |
$[(31, 42)]$ |
1848.g4 |
1848j1 |
1848.g |
1848j |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{4} \cdot 3^{4} \cdot 7 \cdot 11 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.29 |
2B |
$1232$ |
$192$ |
$1$ |
$2.360254557$ |
$1$ |
|
$7$ |
$768$ |
$0.390584$ |
$62140690757632/6237$ |
$0.98642$ |
$4.59102$ |
$[0, 1, 0, -2079, 35802]$ |
\(y^2=x^3+x^2-2079x+35802\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.h.1.2, 56.48.0-56.bu.2.6, $\ldots$ |
$[(42, 156)]$ |
1848.g5 |
1848j4 |
1848.g |
1848j |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{10} \cdot 3^{16} \cdot 7 \cdot 11 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.48.0.29 |
2B |
$1232$ |
$192$ |
$1$ |
$2.360254557$ |
$1$ |
|
$7$ |
$3072$ |
$1.083731$ |
$-17418812548/3314597517$ |
$1.01681$ |
$4.82737$ |
$[0, 1, 0, -544, 88592]$ |
\(y^2=x^3+x^2-544x+88592\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.2, 16.48.0-16.h.1.2, 56.48.0-56.bv.2.7, $\ldots$ |
$[(-13, 306)]$ |
1848.g6 |
1848j6 |
1848.g |
1848j |
$6$ |
$8$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{11} \cdot 3^{2} \cdot 7^{2} \cdot 11^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.48.0.174 |
2B |
$1232$ |
$192$ |
$1$ |
$4.720509114$ |
$1$ |
|
$3$ |
$6144$ |
$1.430304$ |
$146142660369886/94532266521$ |
$1.01155$ |
$5.34977$ |
$[0, 1, 0, 13936, -212640]$ |
\(y^2=x^3+x^2+13936x-212640\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.k.1.6, 56.96.0-56.bc.2.8, 176.96.0.?, $\ldots$ |
$[(115, 1710)]$ |
1848.h1 |
1848f1 |
1848.h |
1848f |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{4} \cdot 3^{7} \cdot 7 \cdot 11^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$462$ |
$2$ |
$0$ |
$0.092711850$ |
$1$ |
|
$12$ |
$672$ |
$0.313465$ |
$575511296/20376279$ |
$0.95539$ |
$3.59495$ |
$[0, 1, 0, 44, -847]$ |
\(y^2=x^3+x^2+44x-847\) |
462.2.0.? |
$[(44, 297)]$ |
1848.i1 |
1848g1 |
1848.i |
1848g |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{4} \cdot 3^{3} \cdot 7^{5} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$462$ |
$2$ |
$0$ |
$0.064780648$ |
$1$ |
|
$10$ |
$480$ |
$0.201626$ |
$-1235663104/4991679$ |
$1.04005$ |
$3.42794$ |
$[0, 1, 0, -56, 441]$ |
\(y^2=x^3+x^2-56x+441\) |
462.2.0.? |
$[(28, 147)]$ |
1848.j1 |
1848i1 |
1848.j |
1848i |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{4} \cdot 3 \cdot 7 \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$462$ |
$2$ |
$0$ |
$0.858509890$ |
$1$ |
|
$4$ |
$96$ |
$-0.636387$ |
$-256/231$ |
$0.83188$ |
$2.08331$ |
$[0, 1, 0, 0, -3]$ |
\(y^2=x^3+x^2-3\) |
462.2.0.? |
$[(2, 3)]$ |
1848.k1 |
1848d1 |
1848.k |
1848d |
$1$ |
$1$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{4} \cdot 3 \cdot 7^{9} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$462$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1440$ |
$0.748445$ |
$-31636584484096/1331669031$ |
$0.95912$ |
$4.51061$ |
$[0, 1, 0, -1660, 26417]$ |
\(y^2=x^3+x^2-1660x+26417\) |
462.2.0.? |
$[ ]$ |
1848.l1 |
1848k3 |
1848.l |
1848k |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{11} \cdot 3^{4} \cdot 7^{4} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$616$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$4096$ |
$1.161922$ |
$2970658109581346/2139291$ |
$1.06890$ |
$5.75020$ |
$[0, 1, 0, -38032, -2867488]$ |
\(y^2=x^3+x^2-38032x-2867488\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 56.24.0-56.z.1.12, 88.24.0.?, 616.48.0.? |
$[ ]$ |
1848.l2 |
1848k4 |
1848.l |
1848k |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{11} \cdot 3^{16} \cdot 7 \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$616$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$4096$ |
$1.161922$ |
$8849350367426/3314597517$ |
$0.97451$ |
$4.97696$ |
$[0, 1, 0, -5472, 90720]$ |
\(y^2=x^3+x^2-5472x+90720\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.1, 56.24.0-56.z.1.10, $\ldots$ |
$[ ]$ |
1848.l3 |
1848k2 |
1848.l |
1848k |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( 2^{10} \cdot 3^{8} \cdot 7^{2} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$616$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$2048$ |
$0.815349$ |
$1478729816932/38900169$ |
$1.03465$ |
$4.64695$ |
$[0, 1, 0, -2392, -44800]$ |
\(y^2=x^3+x^2-2392x-44800\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 28.24.0-28.b.1.1, 88.24.0.?, 616.48.0.? |
$[ ]$ |
1848.l4 |
1848k1 |
1848.l |
1848k |
$4$ |
$4$ |
\( 2^{3} \cdot 3 \cdot 7 \cdot 11 \) |
\( - 2^{8} \cdot 3^{4} \cdot 7 \cdot 11^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$616$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$1024$ |
$0.468775$ |
$9148592/8301447$ |
$0.98816$ |
$3.84628$ |
$[0, 1, 0, 28, -2208]$ |
\(y^2=x^3+x^2+28x-2208\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 14.6.0.b.1, 28.24.0-28.g.1.2, 88.24.0.?, $\ldots$ |
$[ ]$ |