Atkin-Lehner |
2- 5+ 7- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
69580d |
Isogeny class |
Conductor |
69580 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2903040 |
Modular degree for the optimal curve |
Δ |
-1100659158223520000 = -1 · 28 · 54 · 713 · 71 |
Discriminant |
Eigenvalues |
2- -1 5+ 7- -3 -3 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-32721236,72054070936] |
[a1,a2,a3,a4,a6] |
Generators |
[3341:3800:1] |
Generators of the group modulo torsion |
j |
-128642544175666893136/36544720625 |
j-invariant |
L |
3.7343777210614 |
L(r)(E,1)/r! |
Ω |
0.22083853167417 |
Real period |
R |
4.2274979067306 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999987932 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9940d1 |
Quadratic twists by: -7 |