Atkin-Lehner |
2+ 3+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
121968d |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-7044976206576 = -1 · 24 · 39 · 75 · 113 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7+ 11+ -7 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,3861,88209] |
[a1,a2,a3,a4,a6] |
Generators |
[0:297:1] |
Generators of the group modulo torsion |
j |
15185664/16807 |
j-invariant |
L |
2.9636594572447 |
L(r)(E,1)/r! |
Ω |
0.49595263727218 |
Real period |
R |
1.4939225903583 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000212474 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60984i1 121968c1 121968n1 |
Quadratic twists by: -4 -3 -11 |