Atkin-Lehner |
2+ 3+ 5+ 7- 41- |
Signs for the Atkin-Lehner involutions |
Class |
129150m |
Isogeny class |
Conductor |
129150 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
2488320 |
Modular degree for the optimal curve |
Δ |
907910655120000000 = 210 · 39 · 57 · 73 · 412 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7- -4 -6 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-319317,-52091659] |
[a1,a2,a3,a4,a6] |
Generators |
[-391:3783:1] |
Generators of the group modulo torsion |
j |
11707907427243/2952104960 |
j-invariant |
L |
3.6802059805502 |
L(r)(E,1)/r! |
Ω |
0.20455971111742 |
Real period |
R |
1.4992386890309 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999539691 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
129150cm1 25830t1 |
Quadratic twists by: -3 5 |