Atkin-Lehner |
3- 23- 53- |
Signs for the Atkin-Lehner involutions |
Class |
84111d |
Isogeny class |
Conductor |
84111 |
Conductor |
∏ cp |
66 |
Product of Tamagawa factors cp |
deg |
194304 |
Modular degree for the optimal curve |
Δ |
-139250539098243 = -1 · 311 · 234 · 532 |
Discriminant |
Eigenvalues |
0 3- -2 1 0 -3 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-19749,1203176] |
[a1,a2,a3,a4,a6] |
Generators |
[-156:715:1] [-294:10967:8] |
Generators of the group modulo torsion |
j |
-3044175511552/497605923 |
j-invariant |
L |
9.9977309808917 |
L(r)(E,1)/r! |
Ω |
0.56091103685026 |
Real period |
R |
0.27006202852928 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.00000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84111a1 |
Quadratic twists by: -23 |