Atkin-Lehner |
3- 5+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
10725j |
Isogeny class |
Conductor |
10725 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-1832466796875 = -1 · 38 · 59 · 11 · 13 |
Discriminant |
Eigenvalues |
-2 3- 5+ 0 11- 13+ 7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-49908,4275344] |
[a1,a2,a3,a4,a6] |
Generators |
[138:-188:1] |
Generators of the group modulo torsion |
j |
-879878867636224/117277875 |
j-invariant |
L |
2.9750550768829 |
L(r)(E,1)/r! |
Ω |
0.80477990080985 |
Real period |
R |
0.11552285421025 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32175k1 2145a1 117975cb1 |
Quadratic twists by: -3 5 -11 |