Atkin-Lehner |
2+ 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
24640q |
Isogeny class |
Conductor |
24640 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
2608760000 = 26 · 54 · 72 · 113 |
Discriminant |
Eigenvalues |
2+ -2 5+ 7- 11- 4 -8 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1716,-27830] |
[a1,a2,a3,a4,a6] |
Generators |
[77:550:1] |
Generators of the group modulo torsion |
j |
8736724668736/40761875 |
j-invariant |
L |
3.1370487811794 |
L(r)(E,1)/r! |
Ω |
0.74194391979168 |
Real period |
R |
1.4093827028779 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24640d1 12320d2 123200z1 |
Quadratic twists by: -4 8 5 |