Atkin-Lehner |
3+ 5- 31- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
28365f |
Isogeny class |
Conductor |
28365 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-4989694950375 = -1 · 3 · 53 · 312 · 614 |
Discriminant |
Eigenvalues |
1 3+ 5- -2 0 4 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-38442,-2919129] |
[a1,a2,a3,a4,a6] |
Generators |
[92330:-909033:343] |
Generators of the group modulo torsion |
j |
-6282887556567332521/4989694950375 |
j-invariant |
L |
5.0319319697085 |
L(r)(E,1)/r! |
Ω |
0.17046919508889 |
Real period |
R |
9.8393768780038 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85095o1 |
Quadratic twists by: -3 |