Atkin-Lehner |
3- 5+ 7+ 13- 17- |
Signs for the Atkin-Lehner involutions |
Class |
69615k |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
175104 |
Modular degree for the optimal curve |
Δ |
821998256625 = 36 · 53 · 74 · 13 · 172 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7+ 2 13- 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-87908,10053902] |
[a1,a2,a3,a4,a6] |
Generators |
[-270:3883:1] [1206:3065:8] |
Generators of the group modulo torsion |
j |
103056823169347321/1127569625 |
j-invariant |
L |
6.5926757849099 |
L(r)(E,1)/r! |
Ω |
0.80889610292888 |
Real period |
R |
4.0751066552542 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7735d1 |
Quadratic twists by: -3 |