Atkin-Lehner |
2+ 3+ 29+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
129456b |
Isogeny class |
Conductor |
129456 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
47104 |
Modular degree for the optimal curve |
Δ |
-1541044224 = -1 · 211 · 33 · 29 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -3 -2 0 -5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-243,2386] |
[a1,a2,a3,a4,a6] |
Generators |
[-19:12:1] [-9:62:1] |
Generators of the group modulo torsion |
j |
-28697814/27869 |
j-invariant |
L |
10.004798468969 |
L(r)(E,1)/r! |
Ω |
1.3730421236925 |
Real period |
R |
0.4554120324093 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002817 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64728a1 129456d1 |
Quadratic twists by: -4 -3 |