Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cy |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-2187134330508864 = -1 · 26 · 324 · 112 |
Discriminant |
Eigenvalues |
2+ 3- 3 2 11- 1 1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,12309,-2187812] |
[a1,a2,a3,a4,a6] |
Generators |
[4697526532556:102705821552016:10175991463] |
Generators of the group modulo torsion |
j |
36534162368/387420489 |
j-invariant |
L |
9.3793903640089 |
L(r)(E,1)/r! |
Ω |
0.22798693652781 |
Real period |
R |
20.570017095837 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696db1 34848be1 23232ci1 69696dc1 |
Quadratic twists by: -4 8 -3 -11 |