Atkin-Lehner |
3+ 5+ 7+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
45045c |
Isogeny class |
Conductor |
45045 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
196992 |
Modular degree for the optimal curve |
Δ |
-37250385046875 = -1 · 39 · 56 · 7 · 113 · 13 |
Discriminant |
Eigenvalues |
-2 3+ 5+ 7+ 11- 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-32913,2316944] |
[a1,a2,a3,a4,a6] |
Generators |
[64:687:1] [108:148:1] |
Generators of the group modulo torsion |
j |
-200324851273728/1892515625 |
j-invariant |
L |
4.5973471844608 |
L(r)(E,1)/r! |
Ω |
0.6527106744256 |
Real period |
R |
0.5869557223174 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
45045g1 |
Quadratic twists by: -3 |