Atkin-Lehner |
2+ 3- 11- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
61248x |
Isogeny class |
Conductor |
61248 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-44258302623744 = -1 · 219 · 37 · 113 · 29 |
Discriminant |
Eigenvalues |
2+ 3- 3 3 11- -3 -2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2849,-326337] |
[a1,a2,a3,a4,a6] |
Generators |
[451:9504:1] |
Generators of the group modulo torsion |
j |
-9759185353/168832026 |
j-invariant |
L |
11.009036265721 |
L(r)(E,1)/r! |
Ω |
0.2752937022023 |
Real period |
R |
0.4760732065216 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000126 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61248bj1 1914c1 |
Quadratic twists by: -4 8 |