Atkin-Lehner |
2+ 3+ 5- 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
129360bp |
Isogeny class |
Conductor |
129360 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
24847468800 = 28 · 3 · 52 · 76 · 11 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- 11- -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-13540,610912] |
[a1,a2,a3,a4,a6] |
Generators |
[69:20:1] [72:64:1] |
Generators of the group modulo torsion |
j |
9115564624/825 |
j-invariant |
L |
11.389808559469 |
L(r)(E,1)/r! |
Ω |
1.1423695146718 |
Real period |
R |
4.9851682920297 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999954544 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
64680dg1 2640j1 |
Quadratic twists by: -4 -7 |