Atkin-Lehner |
2+ 3+ 11- 29- |
Signs for the Atkin-Lehner involutions |
Class |
61248n |
Isogeny class |
Conductor |
61248 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
-52085515075190784 = -1 · 239 · 33 · 112 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 3 -1 11- 4 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,59711,-9455423] |
[a1,a2,a3,a4,a6] |
Generators |
[639405:45776896:125] |
Generators of the group modulo torsion |
j |
89813071796687/198690471936 |
j-invariant |
L |
7.178317903513 |
L(r)(E,1)/r! |
Ω |
0.1843563786332 |
Real period |
R |
4.8671477743729 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998114 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61248ce1 1914n1 |
Quadratic twists by: -4 8 |