Atkin-Lehner |
2- 3+ 5+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85140a |
Isogeny class |
Conductor |
85140 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1319040 |
Modular degree for the optimal curve |
Δ |
2199013575273717840 = 24 · 33 · 5 · 115 · 436 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 11+ -6 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-725748,227025617] |
[a1,a2,a3,a4,a6] |
j |
97858264278965501952/5090309202022495 |
j-invariant |
L |
0.76971551252909 |
L(r)(E,1)/r! |
Ω |
0.25657184834129 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85140c1 |
Quadratic twists by: -3 |