Atkin-Lehner |
2+ 5- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
13640d |
Isogeny class |
Conductor |
13640 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2048 |
Modular degree for the optimal curve |
Δ |
3410000 = 24 · 54 · 11 · 31 |
Discriminant |
Eigenvalues |
2+ 0 5- 0 11- 2 -2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-122,-511] |
[a1,a2,a3,a4,a6] |
Generators |
[13:10:1] |
Generators of the group modulo torsion |
j |
12551141376/213125 |
j-invariant |
L |
5.0500309744168 |
L(r)(E,1)/r! |
Ω |
1.4379934382772 |
Real period |
R |
1.7559297699116 |
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 |
27280g1 109120a1 122760bk1 68200u1 |
Quadratic twists by: -4 8 -3 5 |