Atkin-Lehner |
2- 3+ 5+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
127200cb |
Isogeny class |
Conductor |
127200 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-50880000000 = -1 · 212 · 3 · 57 · 53 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 -4 -2 -7 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-45133,3705637] |
[a1,a2,a3,a4,a6] |
Generators |
[132:-175:1] [-213:1900:1] |
Generators of the group modulo torsion |
j |
-158867831296/795 |
j-invariant |
L |
8.1906979920638 |
L(r)(E,1)/r! |
Ω |
0.99637785028839 |
Real period |
R |
1.0275592216096 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000007195 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
127200df1 25440w1 |
Quadratic twists by: -4 5 |