Atkin-Lehner |
2- 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
2728d |
Isogeny class |
Conductor |
2728 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
352 |
Modular degree for the optimal curve |
Δ |
-60016 = -1 · 24 · 112 · 31 |
Discriminant |
Eigenvalues |
2- -2 -3 -1 11+ -4 -2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-32,61] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:11:1] [-2:11:1] |
Generators of the group modulo torsion |
j |
-233644288/3751 |
j-invariant |
L |
2.6544988839349 |
L(r)(E,1)/r! |
Ω |
3.5181027262808 |
Real period |
R |
0.18863142227943 |
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 |
5456c1 21824g1 24552f1 68200a1 |
Quadratic twists by: -4 8 -3 5 |