Atkin-Lehner |
3+ 5- 7+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
61005f |
Isogeny class |
Conductor |
61005 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-437877685546875 = -1 · 32 · 512 · 74 · 83 |
Discriminant |
Eigenvalues |
0 3+ 5- 7+ 1 -4 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,11205,-901069] |
[a1,a2,a3,a4,a6] |
Generators |
[65:312:1] [105:1192:1] |
Generators of the group modulo torsion |
j |
64793042714624/182373046875 |
j-invariant |
L |
7.7343908823617 |
L(r)(E,1)/r! |
Ω |
0.27170789520987 |
Real period |
R |
1.18607626958 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999722 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61005r1 |
Quadratic twists by: -7 |