Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cc |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-7492001071104 = -1 · 220 · 310 · 112 |
Discriminant |
Eigenvalues |
2+ 3- -1 -4 11- -5 7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7788,-295504] |
[a1,a2,a3,a4,a6] |
Generators |
[166:1728:1] |
Generators of the group modulo torsion |
j |
-2259169/324 |
j-invariant |
L |
3.7524412898557 |
L(r)(E,1)/r! |
Ω |
0.25210144343593 |
Real period |
R |
1.8605810218802 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997114 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696ge1 2178j1 23232m1 69696ca1 |
Quadratic twists by: -4 8 -3 -11 |