Atkin-Lehner |
2+ 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122694u |
Isogeny class |
Conductor |
122694 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
494208 |
Modular degree for the optimal curve |
Δ |
-511678514977344 = -1 · 26 · 34 · 112 · 138 |
Discriminant |
Eigenvalues |
2+ 3+ -1 0 11- 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-23663,1764261] |
[a1,a2,a3,a4,a6] |
Generators |
[-1130:12733:8] [70:-711:1] |
Generators of the group modulo torsion |
j |
-14846689/5184 |
j-invariant |
L |
7.2065974890792 |
L(r)(E,1)/r! |
Ω |
0.49222571534314 |
Real period |
R |
1.2200699223616 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000007551 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122694ci1 122694cf1 |
Quadratic twists by: -11 13 |