Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
121968r |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-58929205104 = -1 · 24 · 33 · 7 · 117 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7- 11- 1 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-363,-11979] |
[a1,a2,a3,a4,a6] |
Generators |
[36:147:1] |
Generators of the group modulo torsion |
j |
-6912/77 |
j-invariant |
L |
6.453845620308 |
L(r)(E,1)/r! |
Ω |
0.47299040252399 |
Real period |
R |
3.4111926715802 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000063586 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60984bl1 121968o1 11088a1 |
Quadratic twists by: -4 -3 -11 |