Atkin-Lehner |
2+ 3+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
15048a |
Isogeny class |
Conductor |
15048 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
10368 |
Modular degree for the optimal curve |
Δ |
-127427427072 = -1 · 28 · 39 · 113 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 11+ -1 -1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2484,-50652] |
[a1,a2,a3,a4,a6] |
Generators |
[66:270:1] |
Generators of the group modulo torsion |
j |
-336393216/25289 |
j-invariant |
L |
5.4979053648099 |
L(r)(E,1)/r! |
Ω |
0.33667416803299 |
Real period |
R |
2.0412560150261 |
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 |
30096b1 120384i1 15048c1 |
Quadratic twists by: -4 8 -3 |