Atkin-Lehner |
3- 7+ 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
69531j |
Isogeny class |
Conductor |
69531 |
Conductor |
∏ cp |
5 |
Product of Tamagawa factors cp |
deg |
514080 |
Modular degree for the optimal curve |
Δ |
-119767078594779 = -1 · 3 · 78 · 115 · 43 |
Discriminant |
Eigenvalues |
-2 3- 3 7+ 11- -6 5 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-24124,-1543370] |
[a1,a2,a3,a4,a6] |
Generators |
[4465:298204:1] |
Generators of the group modulo torsion |
j |
-269342789632/20775579 |
j-invariant |
L |
5.2886360177279 |
L(r)(E,1)/r! |
Ω |
0.1906941169314 |
Real period |
R |
5.546721737813 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999989521 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69531g1 |
Quadratic twists by: -7 |