Atkin-Lehner |
3+ 7+ 23- 59- |
Signs for the Atkin-Lehner involutions |
Class |
85491b |
Isogeny class |
Conductor |
85491 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
51200 |
Modular degree for the optimal curve |
Δ |
2023315497 = 33 · 74 · 232 · 59 |
Discriminant |
Eigenvalues |
-1 3+ 0 7+ -4 -6 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2000,34850] |
[a1,a2,a3,a4,a6] |
Generators |
[30:19:1] |
Generators of the group modulo torsion |
j |
32752642399875/74937611 |
j-invariant |
L |
2.1641178047577 |
L(r)(E,1)/r! |
Ω |
1.4757701577163 |
Real period |
R |
0.73321641329261 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004564 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85491a1 |
Quadratic twists by: -3 |