Atkin-Lehner |
2- 3+ 17+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
120768ci |
Isogeny class |
Conductor |
120768 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-94975819776 = -1 · 224 · 32 · 17 · 37 |
Discriminant |
Eigenvalues |
2- 3+ -3 -1 -3 -4 17+ -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-101217,12428289] |
[a1,a2,a3,a4,a6] |
Generators |
[75:2292:1] [173:256:1] |
Generators of the group modulo torsion |
j |
-437470189073497/362304 |
j-invariant |
L |
7.0044363541671 |
L(r)(E,1)/r! |
Ω |
0.89083481104131 |
Real period |
R |
0.98284724893803 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000011201 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120768bd1 30192bc1 |
Quadratic twists by: -4 8 |