Atkin-Lehner |
2+ 3+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
53064b |
Isogeny class |
Conductor |
53064 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-234649008 = -1 · 24 · 33 · 112 · 672 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 11- -2 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,54,721] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:21:1] [9:44:1] |
Generators of the group modulo torsion |
j |
40310784/543169 |
j-invariant |
L |
8.9999742275609 |
L(r)(E,1)/r! |
Ω |
1.3047772887289 |
Real period |
R |
1.7244272845076 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
106128b1 53064l1 |
Quadratic twists by: -4 -3 |