Atkin-Lehner |
2- 5- 7+ |
Signs for the Atkin-Lehner involutions |
Class |
78400jr |
Isogeny class |
Conductor |
78400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-20141047808000 = -1 · 226 · 53 · 74 |
Discriminant |
Eigenvalues |
2- -3 5- 7+ 0 2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,980,-215600] |
[a1,a2,a3,a4,a6] |
Generators |
[74:512:1] |
Generators of the group modulo torsion |
j |
1323/256 |
j-invariant |
L |
3.3536959128585 |
L(r)(E,1)/r! |
Ω |
0.32232068751462 |
Real period |
R |
1.3006052829634 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002801 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78400dx1 19600dj1 78400jq1 78400lb1 |
Quadratic twists by: -4 8 5 -7 |