Atkin-Lehner |
3+ 7- 11+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
85701h |
Isogeny class |
Conductor |
85701 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
405504 |
Modular degree for the optimal curve |
Δ |
38890171089 = 34 · 77 · 11 · 53 |
Discriminant |
Eigenvalues |
-1 3+ -2 7- 11+ -2 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-337464,75314616] |
[a1,a2,a3,a4,a6] |
Generators |
[-113:10640:1] |
Generators of the group modulo torsion |
j |
36125835691810033/330561 |
j-invariant |
L |
1.089417848532 |
L(r)(E,1)/r! |
Ω |
0.8012926810806 |
Real period |
R |
2.7191508723685 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000019649 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
12243h1 |
Quadratic twists by: -7 |