Atkin-Lehner |
3- 11- 59- |
Signs for the Atkin-Lehner involutions |
Class |
21417q |
Isogeny class |
Conductor |
21417 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
6336 |
Modular degree for the optimal curve |
Δ |
-5204331 = -1 · 36 · 112 · 59 |
Discriminant |
Eigenvalues |
-2 3- -3 0 11- -4 -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-172,820] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:40:1] [8:-5:1] |
Generators of the group modulo torsion |
j |
-4677849088/43011 |
j-invariant |
L |
4.0543887413854 |
L(r)(E,1)/r! |
Ω |
2.432122414115 |
Real period |
R |
0.27783612082016 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64251s1 21417o1 |
Quadratic twists by: -3 -11 |