Atkin-Lehner |
3+ 11+ 23- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
84249a |
Isogeny class |
Conductor |
84249 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
2780217 = 33 · 112 · 23 · 37 |
Discriminant |
Eigenvalues |
1 3+ 0 0 11+ -4 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-42,79] |
[a1,a2,a3,a4,a6] |
Generators |
[-50:91:8] [70:109:8] |
Generators of the group modulo torsion |
j |
307546875/102971 |
j-invariant |
L |
12.822520413581 |
L(r)(E,1)/r! |
Ω |
2.3488613570737 |
Real period |
R |
5.4590367265306 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998344 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
84249b1 |
Quadratic twists by: -3 |