Atkin-Lehner |
2+ 3- 5+ 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
61710z |
Isogeny class |
Conductor |
61710 |
Conductor |
∏ cp |
54 |
Product of Tamagawa factors cp |
deg |
88128 |
Modular degree for the optimal curve |
Δ |
-244951982550 = -1 · 2 · 39 · 52 · 114 · 17 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 2 11- 2 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1939,40412] |
[a1,a2,a3,a4,a6] |
Generators |
[-44:224:1] |
Generators of the group modulo torsion |
j |
-55025549689/16730550 |
j-invariant |
L |
5.9758564903854 |
L(r)(E,1)/r! |
Ω |
0.93474122255267 |
Real period |
R |
1.0655099590313 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998391 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
61710cn1 |
Quadratic twists by: -11 |