Atkin-Lehner |
2- 3+ 5- 7+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
68880br |
Isogeny class |
Conductor |
68880 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
28929600000000 = 212 · 32 · 58 · 72 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7+ -4 -2 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9360,-230400] |
[a1,a2,a3,a4,a6] |
Generators |
[170:1750:1] [-75:210:1] |
Generators of the group modulo torsion |
j |
22143063655441/7062890625 |
j-invariant |
L |
8.9588738452791 |
L(r)(E,1)/r! |
Ω |
0.49760744974374 |
Real period |
R |
0.56262181727606 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4305m1 |
Quadratic twists by: -4 |