Atkin-Lehner |
2+ 3- 5+ 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69090u |
Isogeny class |
Conductor |
69090 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
1843200 |
Modular degree for the optimal curve |
Δ |
4027218181462425600 = 220 · 34 · 52 · 79 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- -2 -6 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-1249379,-528874594] |
[a1,a2,a3,a4,a6] |
Generators |
[6591:-530144:1] [-5106:26069:8] |
Generators of the group modulo torsion |
j |
1833232627165506841/34230789734400 |
j-invariant |
L |
8.5124379774889 |
L(r)(E,1)/r! |
Ω |
0.14296129037456 |
Real period |
R |
3.7214785359093 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999671 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9870a1 |
Quadratic twists by: -7 |