Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192v |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1523712 |
Modular degree for the optimal curve |
Δ |
-2.2481758785103E+20 |
Discriminant |
Eigenvalues |
2+ 3- -3 1 2 2 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1519341,28629151] |
[a1,a2,a3,a4,a6] |
Generators |
[4048693:241038981:1331] |
Generators of the group modulo torsion |
j |
1257728/729 |
j-invariant |
L |
5.4574670455801 |
L(r)(E,1)/r! |
Ω |
0.10616080190304 |
Real period |
R |
6.4259441191727 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000323 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23064n1 69192w1 |
Quadratic twists by: -3 -31 |