Atkin-Lehner |
3- 5+ 7- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615l |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
261120 |
Modular degree for the optimal curve |
Δ |
-956612429664255 = -1 · 316 · 5 · 7 · 133 · 172 |
Discriminant |
Eigenvalues |
1 3- 5+ 7- -2 13+ 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,2025,1487160] |
[a1,a2,a3,a4,a6] |
Generators |
[-2904:4916:27] |
Generators of the group modulo torsion |
j |
1259362112399/1312225555095 |
j-invariant |
L |
5.7792162141405 |
L(r)(E,1)/r! |
Ω |
0.38742314043826 |
Real period |
R |
7.4585325575861 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001901 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23205n1 |
Quadratic twists by: -3 |