Atkin-Lehner |
2- 3+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
61152bh |
Isogeny class |
Conductor |
61152 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
291840 |
Modular degree for the optimal curve |
Δ |
-6036119212032 = -1 · 212 · 34 · 72 · 135 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- -3 13- -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-208273,36654241] |
[a1,a2,a3,a4,a6] |
Generators |
[247:-468:1] [65:4836:1] |
Generators of the group modulo torsion |
j |
-4978158127432000/30074733 |
j-invariant |
L |
8.6190744068637 |
L(r)(E,1)/r! |
Ω |
0.67311435343758 |
Real period |
R |
0.32011924730367 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999936 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61152u1 122304ct1 61152bp1 |
Quadratic twists by: -4 8 -7 |