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 |
1617.a1 |
1617c1 |
1617.a |
1617c |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3^{5} \cdot 7^{8} \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.283871610$ |
$1$ |
|
$6$ |
$2520$ |
$0.836077$ |
$3584000/29403$ |
$[0, -1, 1, 572, 18906]$ |
\(y^2+y=x^3-x^2+572x+18906\) |
6.2.0.a.1 |
$[(33, 269)]$ |
1617.b1 |
1617i1 |
1617.b |
1617i |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3^{5} \cdot 7^{2} \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.134818892$ |
$1$ |
|
$8$ |
$360$ |
$-0.136878$ |
$3584000/29403$ |
$[0, 1, 1, 12, -52]$ |
\(y^2+y=x^3+x^2+12x-52\) |
6.2.0.a.1 |
$[(6, 16)]$ |
1617.c1 |
1617b1 |
1617.c |
1617b |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3^{7} \cdot 7^{8} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$132$ |
$2$ |
$0$ |
$1.190687554$ |
$1$ |
|
$2$ |
$2352$ |
$0.823755$ |
$17999471/24057$ |
$[1, 1, 1, 979, -13084]$ |
\(y^2+xy+y=x^3+x^2+979x-13084\) |
132.2.0.? |
$[(20, 112)]$ |
1617.d1 |
1617h1 |
1617.d |
1617h |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3^{7} \cdot 7^{2} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$132$ |
$2$ |
$0$ |
$0.136514308$ |
$1$ |
|
$8$ |
$336$ |
$-0.149199$ |
$17999471/24057$ |
$[1, 0, 0, 20, 41]$ |
\(y^2+xy=x^3+20x+41\) |
132.2.0.? |
$[(-1, 5)]$ |
1617.e1 |
1617g5 |
1617.e |
1617g |
$6$ |
$8$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3^{8} \cdot 7^{7} \cdot 11^{2} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.46 |
2B |
$3696$ |
$192$ |
$1$ |
$0.792272677$ |
$1$ |
|
$10$ |
$7680$ |
$1.595745$ |
$10206027697760497/5557167$ |
$[1, 0, 0, -221432, 40087473]$ |
\(y^2+xy=x^3-221432x+40087473\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.n.1.12, 28.24.0-28.h.1.2, 48.48.0-48.e.2.18, $\ldots$ |
$[(-59, 7306)]$ |
1617.e2 |
1617g3 |
1617.e |
1617g |
$6$ |
$8$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3^{4} \cdot 7^{8} \cdot 11^{4} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.24.0.3 |
2Cs |
$1848$ |
$192$ |
$1$ |
$1.584545354$ |
$1$ |
|
$8$ |
$3840$ |
$1.249172$ |
$2533811507137/58110129$ |
$[1, 0, 0, -13917, 618120]$ |
\(y^2+xy=x^3-13917x+618120\) |
2.6.0.a.1, 4.24.0-4.b.1.2, 24.48.0-24.i.1.32, 28.48.0-28.c.1.2, 88.48.0.?, $\ldots$ |
$[(39, 348)]$ |
1617.e3 |
1617g2 |
1617.e |
1617g |
$6$ |
$8$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3^{2} \cdot 7^{10} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.24 |
2Cs |
$1848$ |
$192$ |
$1$ |
$3.169090709$ |
$1$ |
|
$6$ |
$1920$ |
$0.902597$ |
$6570725617/2614689$ |
$[1, 0, 0, -1912, -18145]$ |
\(y^2+xy=x^3-1912x-18145\) |
2.6.0.a.1, 4.12.0.b.1, 8.24.0-4.b.1.5, 24.48.0-24.i.2.5, 28.24.0-4.b.1.3, $\ldots$ |
$[(-13, 74)]$ |
1617.e4 |
1617g1 |
1617.e |
1617g |
$6$ |
$8$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3 \cdot 7^{8} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.4 |
2B |
$3696$ |
$192$ |
$1$ |
$6.338181419$ |
$1$ |
|
$1$ |
$960$ |
$0.556025$ |
$4354703137/1617$ |
$[1, 0, 0, -1667, -26328]$ |
\(y^2+xy=x^3-1667x-26328\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0-8.n.1.8, $\ldots$ |
$[(-1919/9, 6533/9)]$ |
1617.e5 |
1617g6 |
1617.e |
1617g |
$6$ |
$8$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3^{2} \cdot 7^{7} \cdot 11^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.56 |
2B |
$3696$ |
$192$ |
$1$ |
$3.169090709$ |
$1$ |
|
$2$ |
$7680$ |
$1.595745$ |
$3288008303/13504609503$ |
$[1, 0, 0, 1518, 1917747]$ |
\(y^2+xy=x^3+1518x+1917747\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.n.1.10, 14.6.0.b.1, 24.48.0-24.bz.2.6, $\ldots$ |
$[(186, 2847)]$ |
1617.e6 |
1617g4 |
1617.e |
1617g |
$6$ |
$8$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3 \cdot 7^{14} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.4 |
2B |
$3696$ |
$192$ |
$1$ |
$6.338181419$ |
$1$ |
|
$2$ |
$3840$ |
$1.249172$ |
$221115865823/190238433$ |
$[1, 0, 0, 6173, -129718]$ |
\(y^2+xy=x^3+6173x-129718\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.n.1, 16.24.0-8.n.1.8, 24.24.0.bz.1, $\ldots$ |
$[(526, 11932)]$ |
1617.f1 |
1617d2 |
1617.f |
1617d |
$2$ |
$2$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3^{16} \cdot 7^{3} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.27 |
2B |
$616$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$2560$ |
$1.051805$ |
$14553591673375/5208653241$ |
$[1, 1, 0, -3560, 49029]$ |
\(y^2+xy=x^3+x^2-3560x+49029\) |
2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 28.12.0.l.1, 56.24.0.cb.1, $\ldots$ |
$[]$ |
1617.f2 |
1617d1 |
1617.f |
1617d |
$2$ |
$2$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3^{8} \cdot 7^{3} \cdot 11^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.11 |
2B |
$616$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$1280$ |
$0.705232$ |
$98931640625/96059601$ |
$[1, 1, 0, 675, 5832]$ |
\(y^2+xy=x^3+x^2+675x+5832\) |
2.3.0.a.1, 4.12.0.f.1, 14.6.0.b.1, 28.24.0.g.1, 88.24.0.?, $\ldots$ |
$[]$ |
1617.g1 |
1617a1 |
1617.g |
1617a |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3 \cdot 7^{4} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$132$ |
$2$ |
$0$ |
$0.938800690$ |
$1$ |
|
$2$ |
$144$ |
$-0.294179$ |
$-765625/33$ |
$[1, 1, 0, -25, -62]$ |
\(y^2+xy=x^3+x^2-25x-62\) |
132.2.0.? |
$[(6, 4)]$ |
1617.h1 |
1617e1 |
1617.h |
1617e |
$1$ |
$1$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3 \cdot 7^{10} \cdot 11 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$132$ |
$2$ |
$0$ |
$2.994456445$ |
$1$ |
|
$2$ |
$1008$ |
$0.678776$ |
$-765625/33$ |
$[1, 0, 1, -1251, 17539]$ |
\(y^2+xy+y=x^3-1251x+17539\) |
132.2.0.? |
$[(19, 17)]$ |
1617.i1 |
1617f2 |
1617.i |
1617f |
$2$ |
$2$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3^{16} \cdot 7^{9} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.27 |
2B |
$616$ |
$48$ |
$1$ |
$1.000848649$ |
$1$ |
|
$4$ |
$17920$ |
$2.024761$ |
$14553591673375/5208653241$ |
$[1, 0, 1, -174466, -17340319]$ |
\(y^2+xy+y=x^3-174466x-17340319\) |
2.3.0.a.1, 4.6.0.e.1, 8.12.0.r.1, 28.12.0.l.1, 56.24.0.cb.1, $\ldots$ |
$[(-167, 2756)]$ |
1617.i2 |
1617f1 |
1617.i |
1617f |
$2$ |
$2$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3^{8} \cdot 7^{9} \cdot 11^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.11 |
2B |
$616$ |
$48$ |
$1$ |
$2.001697298$ |
$1$ |
|
$3$ |
$8960$ |
$1.678186$ |
$98931640625/96059601$ |
$[1, 0, 1, 33049, -1901203]$ |
\(y^2+xy+y=x^3+33049x-1901203\) |
2.3.0.a.1, 4.12.0.f.1, 14.6.0.b.1, 28.24.0.g.1, 88.24.0.?, $\ldots$ |
$[(537, 12799)]$ |
1617.j1 |
1617j3 |
1617.j |
1617j |
$4$ |
$4$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3^{3} \cdot 7^{6} \cdot 11^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1848$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1728$ |
$0.960323$ |
$347873904937/395307$ |
$[1, 0, 1, -7180, -234517]$ |
\(y^2+xy+y=x^3-7180x-234517\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 28.12.0-4.c.1.2, 84.24.0.?, $\ldots$ |
$[]$ |
1617.j2 |
1617j2 |
1617.j |
1617j |
$4$ |
$4$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3^{6} \cdot 7^{6} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$924$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$864$ |
$0.613750$ |
$169112377/88209$ |
$[1, 0, 1, -565, -1669]$ |
\(y^2+xy+y=x^3-565x-1669\) |
2.6.0.a.1, 12.12.0.a.1, 28.12.0-2.a.1.1, 44.12.0.b.1, 84.24.0.?, $\ldots$ |
$[]$ |
1617.j3 |
1617j1 |
1617.j |
1617j |
$4$ |
$4$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( 3^{3} \cdot 7^{6} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1848$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$432$ |
$0.267176$ |
$30664297/297$ |
$[1, 0, 1, -320, 2153]$ |
\(y^2+xy+y=x^3-320x+2153\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 56.12.0-4.c.1.5, 66.6.0.a.1, $\ldots$ |
$[]$ |
1617.j4 |
1617j4 |
1617.j |
1617j |
$4$ |
$4$ |
\( 3 \cdot 7^{2} \cdot 11 \) |
\( - 3^{12} \cdot 7^{6} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1848$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1728$ |
$0.960323$ |
$9090072503/5845851$ |
$[1, 0, 1, 2130, -12449]$ |
\(y^2+xy+y=x^3+2130x-12449\) |
2.3.0.a.1, 4.6.0.c.1, 22.6.0.a.1, 24.12.0.ba.1, 28.12.0-4.c.1.1, $\ldots$ |
$[]$ |