Atkin-Lehner |
2- 3- 5+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
85680dt |
Isogeny class |
Conductor |
85680 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
66392166881250000 = 24 · 37 · 58 · 75 · 172 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ -4 -2 17+ -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-119388,9920563] |
[a1,a2,a3,a4,a6] |
Generators |
[293:306:1] |
Generators of the group modulo torsion |
j |
16134601070166016/5692058203125 |
j-invariant |
L |
3.994023751242 |
L(r)(E,1)/r! |
Ω |
0.31943310096772 |
Real period |
R |
3.1258687178683 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000439 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
21420p1 28560du1 |
Quadratic twists by: -4 -3 |