Atkin-Lehner |
3+ 5+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
75075d |
Isogeny class |
Conductor |
75075 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
430080 |
Modular degree for the optimal curve |
Δ |
-140714245546875 = -1 · 32 · 57 · 72 · 11 · 135 |
Discriminant |
Eigenvalues |
0 3+ 5+ 7+ 11+ 13- -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-500533,136468593] |
[a1,a2,a3,a4,a6] |
Generators |
[-603:14787:1] [307:-3413:1] |
Generators of the group modulo torsion |
j |
-887570176172621824/9005711715 |
j-invariant |
L |
7.4143859804892 |
L(r)(E,1)/r! |
Ω |
0.52580419836134 |
Real period |
R |
0.1762629987462 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999575 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15015j1 |
Quadratic twists by: 5 |