Atkin-Lehner |
2- 3- 5+ 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
69030bm |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
-3958732440000 = -1 · 26 · 37 · 54 · 13 · 592 |
Discriminant |
Eigenvalues |
2- 3- 5+ -2 0 13- -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-35393,2573457] |
[a1,a2,a3,a4,a6] |
Generators |
[83:408:1] |
Generators of the group modulo torsion |
j |
-6725689416955081/5430360000 |
j-invariant |
L |
7.8267187576925 |
L(r)(E,1)/r! |
Ω |
0.77719353749877 |
Real period |
R |
0.41960369690706 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000729 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23010e1 |
Quadratic twists by: -3 |