Atkin-Lehner |
2+ 3+ 7+ 23- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
84042b |
Isogeny class |
Conductor |
84042 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-3529764 = -1 · 22 · 33 · 72 · 23 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7+ -3 -5 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-15,97] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:11:1] [6:11:1] |
Generators of the group modulo torsion |
j |
-14348907/130732 |
j-invariant |
L |
7.1727236028917 |
L(r)(E,1)/r! |
Ω |
2.1366100729374 |
Real period |
R |
0.41963223038221 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999741 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84042bb1 |
Quadratic twists by: -3 |