Atkin-Lehner |
2+ 3+ 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
4080d |
Isogeny class |
Conductor |
4080 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
53760 |
Modular degree for the optimal curve |
Δ |
-488191408750944000 = -1 · 28 · 37 · 53 · 178 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 4 0 2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-20236,-33628064] |
[a1,a2,a3,a4,a6] |
Generators |
[1238131197079020:-7445500609661912:3465573357637] |
Generators of the group modulo torsion |
j |
-3579968623693264/1906997690433375 |
j-invariant |
L |
3.3040547961705 |
L(r)(E,1)/r! |
Ω |
0.13249507993248 |
Real period |
R |
24.937188594884 |
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 |
2040f1 16320cx1 12240z1 20400bk1 |
Quadratic twists by: -4 8 -3 5 |