Atkin-Lehner |
3- 7- 17+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72471k |
Isogeny class |
Conductor |
72471 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-2924466252897 = -1 · 3 · 711 · 17 · 29 |
Discriminant |
Eigenvalues |
-1 3- 0 7- -3 4 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-61398,5851173] |
[a1,a2,a3,a4,a6] |
Generators |
[3909:-754:27] |
Generators of the group modulo torsion |
j |
-217569787548625/24857553 |
j-invariant |
L |
4.2163688435704 |
L(r)(E,1)/r! |
Ω |
0.77159516128286 |
Real period |
R |
1.3661208151209 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002063 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10353b1 |
Quadratic twists by: -7 |