Atkin-Lehner |
2+ 3- 13- 73- |
Signs for the Atkin-Lehner involutions |
Class |
68328d |
Isogeny class |
Conductor |
68328 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
108544 |
Modular degree for the optimal curve |
Δ |
2302380288 = 28 · 36 · 132 · 73 |
Discriminant |
Eigenvalues |
2+ 3- 2 -2 -6 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-36999,2739258] |
[a1,a2,a3,a4,a6] |
Generators |
[-114:2340:1] [99:216:1] |
Generators of the group modulo torsion |
j |
30014158880592/12337 |
j-invariant |
L |
10.780623357609 |
L(r)(E,1)/r! |
Ω |
1.184060323316 |
Real period |
R |
2.276198084114 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999809 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7592c1 |
Quadratic twists by: -3 |