Atkin-Lehner |
3+ 5- 17+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
75225i |
Isogeny class |
Conductor |
75225 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
497280 |
Modular degree for the optimal curve |
Δ |
1238162361328125 = 37 · 59 · 173 · 59 |
Discriminant |
Eigenvalues |
2 3+ 5- -1 -4 -3 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-27208,352443] |
[a1,a2,a3,a4,a6] |
Generators |
[-2974944:47083491:32768] |
Generators of the group modulo torsion |
j |
1140511035392/633939129 |
j-invariant |
L |
8.300433236461 |
L(r)(E,1)/r! |
Ω |
0.42032074492332 |
Real period |
R |
9.8739276311089 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002419 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75225x1 |
Quadratic twists by: 5 |