Atkin-Lehner |
11- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
3509a |
Isogeny class |
Conductor |
3509 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
240 |
Modular degree for the optimal curve |
Δ |
3509 = 112 · 29 |
Discriminant |
Eigenvalues |
-2 0 -2 -1 11- -3 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-11,-14] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:0:1] [4:2:1] |
Generators of the group modulo torsion |
j |
1216512/29 |
j-invariant |
L |
2.141309515953 |
L(r)(E,1)/r! |
Ω |
2.6253194433045 |
Real period |
R |
0.81563770131409 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
56144l1 31581p1 87725e1 3509d1 |
Quadratic twists by: -4 -3 5 -11 |