Atkin-Lehner |
2- 3+ 43- 47- |
Signs for the Atkin-Lehner involutions |
Class |
48504j |
Isogeny class |
Conductor |
48504 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
84480 |
Modular degree for the optimal curve |
Δ |
77486886144 = 28 · 34 · 433 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -3 -2 -6 0 5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-11292,465444] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:774:1] [42:252:1] |
Generators of the group modulo torsion |
j |
622063636754128/302683149 |
j-invariant |
L |
6.099280695624 |
L(r)(E,1)/r! |
Ω |
1.0714367794464 |
Real period |
R |
0.23719243218658 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999982 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
97008j1 |
Quadratic twists by: -4 |