| 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 |
| 1694.a1 |
1694a1 |
1694.a |
1694a |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2 \cdot 7 \cdot 11^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$56$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1056$ |
$0.507980$ |
$24167/14$ |
$0.97903$ |
$3.93766$ |
$[1, 1, 0, 361, 235]$ |
\(y^2+xy=x^3+x^2+361x+235\) |
56.2.0.b.1 |
$[]$ |
| 1694.b1 |
1694c1 |
1694.b |
1694c |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{6} \cdot 7^{4} \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.8.0.2 |
|
$44$ |
$16$ |
$0$ |
$0.301960962$ |
$1$ |
|
$6$ |
$288$ |
$0.087654$ |
$-115538049/153664$ |
$1.03468$ |
$3.30259$ |
$[1, -1, 0, -50, -236]$ |
\(y^2+xy=x^3-x^2-50x-236\) |
4.8.0.b.1, 44.16.0-4.b.1.1 |
$[(12, 22)]$ |
| 1694.c1 |
1694d4 |
1694.c |
1694d |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{4} \cdot 11^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.15 |
2B |
$616$ |
$48$ |
$0$ |
$1.942370855$ |
$1$ |
|
$4$ |
$11520$ |
$1.826120$ |
$15226621995131793/2324168$ |
$1.03578$ |
$6.94691$ |
$[1, -1, 0, -624806, 190249164]$ |
\(y^2+xy=x^3-x^2-624806x+190249164\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 44.12.0-4.c.1.1, 56.24.0.v.1, $\ldots$ |
$[(245, 7077)]$ |
| 1694.c2 |
1694d3 |
1694.c |
1694d |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( 2^{3} \cdot 7 \cdot 11^{14} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$616$ |
$48$ |
$0$ |
$7.769483423$ |
$1$ |
|
$0$ |
$11520$ |
$1.826120$ |
$24331017010833/12004097336$ |
$1.13408$ |
$6.08084$ |
$[1, -1, 0, -73046, -2899748]$ |
\(y^2+xy=x^3-x^2-73046x-2899748\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 56.24.0.bp.1, 88.24.0.?, $\ldots$ |
$[(-419/3, 17671/3)]$ |
| 1694.c3 |
1694d2 |
1694.c |
1694d |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( 2^{6} \cdot 7^{2} \cdot 11^{10} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.3 |
2Cs |
$616$ |
$48$ |
$0$ |
$3.884741711$ |
$1$ |
|
$4$ |
$5760$ |
$1.479548$ |
$3750606459153/45914176$ |
$1.08438$ |
$5.82935$ |
$[1, -1, 0, -39166, 2961492]$ |
\(y^2+xy=x^3-x^2-39166x+2961492\) |
2.6.0.a.1, 8.12.0.a.1, 28.12.0.b.1, 44.12.0-2.a.1.1, 56.24.0.d.1, $\ldots$ |
$[(61, 862)]$ |
| 1694.c4 |
1694d1 |
1694.c |
1694d |
$4$ |
$4$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{12} \cdot 7 \cdot 11^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$616$ |
$48$ |
$0$ |
$1.942370855$ |
$1$ |
|
$3$ |
$2880$ |
$1.132973$ |
$-5545233/3469312$ |
$1.05747$ |
$4.96345$ |
$[1, -1, 0, -446, 119444]$ |
\(y^2+xy=x^3-x^2-446x+119444\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 14.6.0.b.1, 28.12.0.g.1, $\ldots$ |
$[(223, 3216)]$ |
| 1694.d1 |
1694b1 |
1694.d |
1694b |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{9} \cdot 7^{5} \cdot 11^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$56$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$4320$ |
$0.825889$ |
$-8773917273/8605184$ |
$1.04428$ |
$4.50284$ |
$[1, -1, 0, -1051, 21797]$ |
\(y^2+xy=x^3-x^2-1051x+21797\) |
56.2.0.b.1 |
$[]$ |
| 1694.e1 |
1694f6 |
1694.e |
1694f |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( 2^{9} \cdot 7^{2} \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$5544$ |
$864$ |
$21$ |
$0.420859867$ |
$1$ |
|
$10$ |
$8640$ |
$1.612049$ |
$2251439055699625/25088$ |
$1.06489$ |
$6.68981$ |
$[1, 0, 0, -330393, 73068601]$ |
\(y^2+xy=x^3-330393x+73068601\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[(362, 787)]$ |
| 1694.e2 |
1694f5 |
1694.e |
1694f |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{18} \cdot 7 \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$5544$ |
$864$ |
$21$ |
$0.210429933$ |
$1$ |
|
$13$ |
$4320$ |
$1.265474$ |
$-548347731625/1835008$ |
$1.02933$ |
$5.57151$ |
$[1, 0, 0, -20633, 1142329]$ |
\(y^2+xy=x^3-20633x+1142329\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[(10, 963)]$ |
| 1694.e3 |
1694f4 |
1694.e |
1694f |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{6} \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.12.0.1 |
2B, 3Cs |
$5544$ |
$864$ |
$21$ |
$1.262579603$ |
$1$ |
|
$6$ |
$2880$ |
$1.062742$ |
$4956477625/941192$ |
$1.00821$ |
$4.93774$ |
$[1, 0, 0, -4298, 88540]$ |
\(y^2+xy=x^3-4298x+88540\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 24.72.1.h.1, $\ldots$ |
$[(54, 94)]$ |
| 1694.e4 |
1694f2 |
1694.e |
1694f |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( 2 \cdot 7^{2} \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$5544$ |
$864$ |
$21$ |
$3.787738810$ |
$1$ |
|
$0$ |
$960$ |
$0.513436$ |
$128787625/98$ |
$0.96763$ |
$4.44677$ |
$[1, 0, 0, -1273, -17577]$ |
\(y^2+xy=x^3-1273x-17577\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[(403/2, 7099/2)]$ |
| 1694.e5 |
1694f1 |
1694.e |
1694f |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{2} \cdot 7 \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$5544$ |
$864$ |
$21$ |
$1.893869405$ |
$1$ |
|
$3$ |
$480$ |
$0.166863$ |
$-15625/28$ |
$1.01712$ |
$3.42363$ |
$[1, 0, 0, -63, -395]$ |
\(y^2+xy=x^3-63x-395\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[(98, 919)]$ |
| 1694.e6 |
1694f3 |
1694.e |
1694f |
$6$ |
$18$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{6} \cdot 7^{3} \cdot 11^{6} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.12.0.1 |
2B, 3Cs |
$5544$ |
$864$ |
$21$ |
$0.631289801$ |
$1$ |
|
$9$ |
$1440$ |
$0.716169$ |
$9938375/21952$ |
$0.98695$ |
$4.24150$ |
$[1, 0, 0, 542, 8196]$ |
\(y^2+xy=x^3+542x+8196\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$ |
$[(10, 116)]$ |
| 1694.f1 |
1694h1 |
1694.f |
1694h |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2 \cdot 7 \cdot 11^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$56$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$96$ |
$-0.690968$ |
$24167/14$ |
$0.97903$ |
$2.00253$ |
$[1, 1, 1, 3, 1]$ |
\(y^2+xy+y=x^3+x^2+3x+1\) |
56.2.0.b.1 |
$[]$ |
| 1694.g1 |
1694g2 |
1694.g |
1694g |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( 2^{3} \cdot 7^{2} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5760$ |
$1.246962$ |
$11422548526761/4312$ |
$1.11135$ |
$5.97914$ |
$[1, -1, 1, -56772, -5192305]$ |
\(y^2+xy+y=x^3-x^2-56772x-5192305\) |
2.3.0.a.1, 28.6.0.c.1, 88.6.0.?, 616.12.0.? |
$[]$ |
| 1694.g2 |
1694g1 |
1694.g |
1694g |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{6} \cdot 7 \cdot 11^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$616$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$2880$ |
$0.900389$ |
$-2749884201/54208$ |
$1.01159$ |
$4.86300$ |
$[1, -1, 1, -3532, -81265]$ |
\(y^2+xy+y=x^3-x^2-3532x-81265\) |
2.3.0.a.1, 14.6.0.b.1, 88.6.0.?, 616.12.0.? |
$[]$ |
| 1694.h1 |
1694e1 |
1694.h |
1694e |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{6} \cdot 7^{4} \cdot 11^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.16.0.2 |
|
$4$ |
$16$ |
$0$ |
$0.175571424$ |
$1$ |
|
$6$ |
$3168$ |
$1.286602$ |
$-115538049/153664$ |
$1.03468$ |
$5.23772$ |
$[1, -1, 1, -6073, 332313]$ |
\(y^2+xy+y=x^3-x^2-6073x+332313\) |
4.16.0-4.b.1.1 |
$[(333, 5762)]$ |
| 1694.i1 |
1694i2 |
1694.i |
1694i |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( 2^{2} \cdot 7^{2} \cdot 11^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$3840$ |
$1.106632$ |
$1426487591593/2156$ |
$0.95006$ |
$5.69932$ |
$[1, 1, 1, -28377, 1828091]$ |
\(y^2+xy+y=x^3+x^2-28377x+1828091\) |
2.3.0.a.1, 28.6.0.c.1, 44.6.0.a.1, 308.12.0.? |
$[]$ |
| 1694.i2 |
1694i1 |
1694.i |
1694i |
$2$ |
$2$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{4} \cdot 7 \cdot 11^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$308$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1920$ |
$0.760059$ |
$-338608873/13552$ |
$0.87448$ |
$4.58578$ |
$[1, 1, 1, -1757, 28579]$ |
\(y^2+xy+y=x^3+x^2-1757x+28579\) |
2.3.0.a.1, 14.6.0.b.1, 44.6.0.b.1, 308.12.0.? |
$[]$ |
| 1694.j1 |
1694j1 |
1694.j |
1694j |
$1$ |
$1$ |
\( 2 \cdot 7 \cdot 11^{2} \) |
\( - 2^{9} \cdot 7^{5} \cdot 11^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$56$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$47520$ |
$2.024837$ |
$-8773917273/8605184$ |
$1.04428$ |
$6.43797$ |
$[1, -1, 1, -127194, -28630247]$ |
\(y^2+xy+y=x^3-x^2-127194x-28630247\) |
56.2.0.b.1 |
$[]$ |
