Atkin-Lehner |
3- 11+ 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
75933d |
Isogeny class |
Conductor |
75933 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
1743360 |
Modular degree for the optimal curve |
Δ |
20179339629632469 = 37 · 112 · 135 · 593 |
Discriminant |
Eigenvalues |
-2 3- -3 0 11+ 13- -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-1523289,723606070] |
[a1,a2,a3,a4,a6] |
Generators |
[-764:-37967:1] [-7646:289155:8] |
Generators of the group modulo torsion |
j |
536220115289063206912/27680849972061 |
j-invariant |
L |
4.4473009811897 |
L(r)(E,1)/r! |
Ω |
0.36290978170304 |
Real period |
R |
0.10212136287869 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000105 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25311c1 |
Quadratic twists by: -3 |