Atkin-Lehner |
2- 3+ 5- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69300n |
Isogeny class |
Conductor |
69300 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
608256 |
Modular degree for the optimal curve |
Δ |
302053354856946000 = 24 · 39 · 53 · 78 · 113 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7+ 11+ 2 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-167940,-1585575] |
[a1,a2,a3,a4,a6] |
Generators |
[810:19845:1] |
Generators of the group modulo torsion |
j |
13306531627008/7672950131 |
j-invariant |
L |
6.1454272046383 |
L(r)(E,1)/r! |
Ω |
0.2570666593408 |
Real period |
R |
3.9843279179771 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999985067 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69300q1 69300t1 |
Quadratic twists by: -3 5 |