Atkin-Lehner |
2- 3+ 5+ 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
21420c |
Isogeny class |
Conductor |
21420 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4257792 |
Modular degree for the optimal curve |
Δ |
1873852518056400 = 24 · 39 · 52 · 77 · 172 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ -4 -4 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2142035388,-38158217199387] |
[a1,a2,a3,a4,a6] |
Generators |
[-545300159114726745372989024007989962072651541340114037033556:-3521109126032386188193620351713130988203319255545079223:20407177431842094726029262179749619256941749057827567808] |
Generators of the group modulo torsion |
j |
3451376687017714259756433408/5950098175 |
j-invariant |
L |
3.8143158128725 |
L(r)(E,1)/r! |
Ω |
0.022191818629764 |
Real period |
R |
85.93968517201 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85680cy1 21420g1 107100h1 |
Quadratic twists by: -4 -3 5 |