Atkin-Lehner |
2- 3- 7- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
53424bm |
Isogeny class |
Conductor |
53424 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-46031308259328 = -1 · 216 · 36 · 73 · 532 |
Discriminant |
Eigenvalues |
2- 3- -4 7- -4 2 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-9147,468970] |
[a1,a2,a3,a4,a6] |
Generators |
[-97:666:1] [-51:896:1] |
Generators of the group modulo torsion |
j |
-28344726649/15415792 |
j-invariant |
L |
7.7747820942534 |
L(r)(E,1)/r! |
Ω |
0.59308396156019 |
Real period |
R |
1.0924229111681 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999961 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6678k1 5936r1 |
Quadratic twists by: -4 -3 |