Atkin-Lehner |
2- 3+ 7+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
7728i |
Isogeny class |
Conductor |
7728 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
47520 |
Modular degree for the optimal curve |
Δ |
-312853007432448 = -1 · 28 · 315 · 7 · 233 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ -3 2 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-478493,-127241151] |
[a1,a2,a3,a4,a6] |
Generators |
[6441:513774:1] |
Generators of the group modulo torsion |
j |
-47327266415721472000/1222082060283 |
j-invariant |
L |
3.2930347783309 |
L(r)(E,1)/r! |
Ω |
0.09076113397377 |
Real period |
R |
6.0470721959074 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1932b1 30912bz1 23184bg1 54096de1 |
Quadratic twists by: -4 8 -3 -7 |