Atkin-Lehner |
11- 13- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
111683d |
Isogeny class |
Conductor |
111683 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
15828480 |
Modular degree for the optimal curve |
Δ |
-168556919002327427 = -1 · 118 · 133 · 713 |
Discriminant |
Eigenvalues |
2 -1 4 -4 11- 13- -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-74876776,-249359176661] |
[a1,a2,a3,a4,a6] |
Generators |
[86359471157979675332579630:10408737475959266802655784649:4515549149973899647000] |
Generators of the group modulo torsion |
j |
-26206499626995248533504/95145986507 |
j-invariant |
L |
11.709428890488 |
L(r)(E,1)/r! |
Ω |
0.025661543462919 |
Real period |
R |
38.025216304077 |
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 |
10153b1 |
Quadratic twists by: -11 |