Atkin-Lehner |
2+ 3- 5+ 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
75240j |
Isogeny class |
Conductor |
75240 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
229376 |
Modular degree for the optimal curve |
Δ |
137124900000000 = 28 · 38 · 58 · 11 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 4 11- -2 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-13143,-137558] |
[a1,a2,a3,a4,a6] |
Generators |
[-30219:198976:343] |
Generators of the group modulo torsion |
j |
1345363813456/734765625 |
j-invariant |
L |
7.7686874967027 |
L(r)(E,1)/r! |
Ω |
0.47610580526338 |
Real period |
R |
8.1585725379264 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000984 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25080t1 |
Quadratic twists by: -3 |