Atkin-Lehner |
2+ 3- 5- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
61920r |
Isogeny class |
Conductor |
61920 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
7617321000000 = 26 · 311 · 56 · 43 |
Discriminant |
Eigenvalues |
2+ 3- 5- 2 6 2 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-32097,2209336] |
[a1,a2,a3,a4,a6] |
Generators |
[-13:1620:1] |
Generators of the group modulo torsion |
j |
78380771974336/163265625 |
j-invariant |
L |
8.4576968463019 |
L(r)(E,1)/r! |
Ω |
0.74262736062764 |
Real period |
R |
0.94907366451959 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000025 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
61920bb1 123840fi1 20640u1 |
Quadratic twists by: -4 8 -3 |