Atkin-Lehner |
2+ 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
45600p |
Isogeny class |
Conductor |
45600 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
-5609655000000 = -1 · 26 · 310 · 57 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 -4 -6 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3258,133488] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:450:1] [-18:432:1] |
Generators of the group modulo torsion |
j |
-3825694144/5609655 |
j-invariant |
L |
10.178167990861 |
L(r)(E,1)/r! |
Ω |
0.68398931225665 |
Real period |
R |
0.74402975371643 |
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 |
45600bf1 91200bh1 9120o1 |
Quadratic twists by: -4 8 5 |