Atkin-Lehner |
2- 3- 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744cr |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
1594678991298624 = 26 · 36 · 710 · 112 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 11- 2 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-29514,-352584] |
[a1,a2,a3,a4,a6] |
Generators |
[-159:588:1] |
Generators of the group modulo torsion |
j |
377619516352/211789809 |
j-invariant |
L |
6.0263353638836 |
L(r)(E,1)/r! |
Ω |
0.39159408597361 |
Real period |
R |
2.5648733300387 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999937 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
51744l1 103488u2 7392l1 |
Quadratic twists by: -4 8 -7 |