Atkin-Lehner |
3- 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
6633g |
Isogeny class |
Conductor |
6633 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
137088 |
Modular degree for the optimal curve |
Δ |
-8395406258255379 = -1 · 323 · 113 · 67 |
Discriminant |
Eigenvalues |
2 3- 3 -3 11- -5 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-865371,309881443] |
[a1,a2,a3,a4,a6] |
Generators |
[4274:1679:8] |
Generators of the group modulo torsion |
j |
-98311244861358051328/11516332315851 |
j-invariant |
L |
8.3314665449796 |
L(r)(E,1)/r! |
Ω |
0.39760159459077 |
Real period |
R |
3.4923847801109 |
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 |
106128bl1 2211d1 72963r1 |
Quadratic twists by: -4 -3 -11 |