Atkin-Lehner |
3+ 5+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
50325g |
Isogeny class |
Conductor |
50325 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
78336 |
Modular degree for the optimal curve |
Δ |
-209320546875 = -1 · 3 · 57 · 114 · 61 |
Discriminant |
Eigenvalues |
-2 3+ 5+ -3 11- 4 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,1092,16718] |
[a1,a2,a3,a4,a6] |
Generators |
[-13:12:1] [2:137:1] |
Generators of the group modulo torsion |
j |
9208180736/13396515 |
j-invariant |
L |
4.2023112714425 |
L(r)(E,1)/r! |
Ω |
0.67809528078949 |
Real period |
R |
0.38732676941707 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10065j1 |
Quadratic twists by: 5 |