Atkin-Lehner |
2+ 3+ 7+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
85008h |
Isogeny class |
Conductor |
85008 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
63767986128 = 24 · 38 · 74 · 11 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ 11- 2 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1407,16758] |
[a1,a2,a3,a4,a6] |
Generators |
[20670:258552:125] |
Generators of the group modulo torsion |
j |
19266137356288/3985499133 |
j-invariant |
L |
6.4566122029246 |
L(r)(E,1)/r! |
Ω |
1.0451699113441 |
Real period |
R |
6.1775718303742 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001008 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42504y1 |
Quadratic twists by: -4 |