Atkin-Lehner |
2- 3+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
11712z |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
69888 |
Modular degree for the optimal curve |
Δ |
-3263292764061696 = -1 · 225 · 313 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 1 -2 2 -4 1 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-454145,117982113] |
[a1,a2,a3,a4,a6] |
Generators |
[469:2816:1] |
Generators of the group modulo torsion |
j |
-39515579724486529/12448473984 |
j-invariant |
L |
3.874363245267 |
L(r)(E,1)/r! |
Ω |
0.43818649472043 |
Real period |
R |
2.2104533640059 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11712n1 2928l1 35136cl1 |
Quadratic twists by: -4 8 -3 |