Atkin-Lehner |
2+ 5+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
49600n |
Isogeny class |
Conductor |
49600 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1290240 |
Modular degree for the optimal curve |
Δ |
-23832800000000000 = -1 · 214 · 511 · 313 |
Discriminant |
Eigenvalues |
2+ 3 5+ -2 2 -2 1 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3845200,-2902204000] |
[a1,a2,a3,a4,a6] |
Generators |
[109970444183745002293313696993435617446907267924251527293946355:12058291654124005980748048125968625335490662892677659106200227025:8901988670590433701272551230870712914922583139936597338363] |
Generators of the group modulo torsion |
j |
-24560689104608256/93096875 |
j-invariant |
L |
10.442268675932 |
L(r)(E,1)/r! |
Ω |
0.053906325187244 |
Real period |
R |
96.855690307779 |
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 |
49600cm1 6200j1 9920e1 |
Quadratic twists by: -4 8 5 |