Atkin-Lehner |
2- 3- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
121968fb |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-1431956645247744 = -1 · 28 · 36 · 78 · 113 |
Discriminant |
Eigenvalues |
2- 3- -1 7- 11+ 0 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,17952,1567676] |
[a1,a2,a3,a4,a6] |
Generators |
[-22:1078:1] [146:2702:1] |
Generators of the group modulo torsion |
j |
2575826944/5764801 |
j-invariant |
L |
11.867937910212 |
L(r)(E,1)/r! |
Ω |
0.33303904557422 |
Real period |
R |
1.1136023379692 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999975096 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
30492i1 13552v1 121968di1 |
Quadratic twists by: -4 -3 -11 |