Atkin-Lehner |
2- 3+ 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
39072k |
Isogeny class |
Conductor |
39072 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
26021952 = 26 · 33 · 11 · 372 |
Discriminant |
Eigenvalues |
2- 3+ -2 2 11+ -6 -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-74,0] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:4:1] |
Generators of the group modulo torsion |
j |
709732288/406593 |
j-invariant |
L |
3.7389462360158 |
L(r)(E,1)/r! |
Ω |
1.7635189918092 |
Real period |
R |
2.1201621606463 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39072g1 78144bj1 117216t1 |
Quadratic twists by: -4 8 -3 |