Atkin-Lehner |
3- 5+ 11- 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
122265o |
Isogeny class |
Conductor |
122265 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
1209600 |
Modular degree for the optimal curve |
Δ |
780830824670325 = 36 · 52 · 113 · 13 · 195 |
Discriminant |
Eigenvalues |
-2 3- 5+ -1 11- 13+ -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-199263,34209994] |
[a1,a2,a3,a4,a6] |
Generators |
[-3262:55229:8] [-61:6792:1] |
Generators of the group modulo torsion |
j |
1200262333794144256/1071098524925 |
j-invariant |
L |
5.9793098882551 |
L(r)(E,1)/r! |
Ω |
0.50095293053813 |
Real period |
R |
0.19893119454451 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999921455 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13585h1 |
Quadratic twists by: -3 |