Atkin-Lehner |
2+ 3+ 7- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
86688f |
Isogeny class |
Conductor |
86688 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
203890176 = 29 · 33 · 73 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7- -2 -5 -5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-243,1286] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:42:1] [5:14:1] |
Generators of the group modulo torsion |
j |
114791256/14749 |
j-invariant |
L |
10.40367831767 |
L(r)(E,1)/r! |
Ω |
1.7185962066696 |
Real period |
R |
0.50446590640946 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998815 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86688bc1 86688be1 |
Quadratic twists by: -4 -3 |