Atkin-Lehner |
2+ 5+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
24640d |
Isogeny class |
Conductor |
24640 |
Conductor |
∏ cp |
4 |
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 |
[1821:12500:27] |
Generators of the group modulo torsion |
j |
8736724668736/40761875 |
j-invariant |
L |
6.8510596120973 |
L(r)(E,1)/r! |
Ω |
1.4491057782419 |
Real period |
R |
4.7277843446386 |
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 |
24640q1 12320i2 123200bu1 |
Quadratic twists by: -4 8 5 |