Atkin-Lehner |
2+ 3+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
121968x |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
5357200464 = 24 · 33 · 7 · 116 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- 11- 6 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-726,6655] |
[a1,a2,a3,a4,a6] |
Generators |
[207:2954:1] |
Generators of the group modulo torsion |
j |
55296/7 |
j-invariant |
L |
7.0139695014972 |
L(r)(E,1)/r! |
Ω |
1.3094610435235 |
Real period |
R |
5.356378922183 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999551581 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
60984g1 121968v1 1008b1 |
Quadratic twists by: -4 -3 -11 |