Atkin-Lehner |
2- 3+ 5+ 11+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
122100b |
Isogeny class |
Conductor |
122100 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
211968 |
Modular degree for the optimal curve |
Δ |
-847068750000 = -1 · 24 · 32 · 58 · 11 · 372 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 11+ -6 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4533,127062] |
[a1,a2,a3,a4,a6] |
Generators |
[33:-111:1] [-18:450:1] |
Generators of the group modulo torsion |
j |
-41213231104/3388275 |
j-invariant |
L |
8.4125520437883 |
L(r)(E,1)/r! |
Ω |
0.87230640010839 |
Real period |
R |
0.80366944839221 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000003494 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24420k1 |
Quadratic twists by: 5 |