Atkin-Lehner |
2- 3+ 19+ 79- |
Signs for the Atkin-Lehner involutions |
Class |
72048k |
Isogeny class |
Conductor |
72048 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-3229668605952 = -1 · 222 · 33 · 192 · 79 |
Discriminant |
Eigenvalues |
2- 3+ 0 -1 1 1 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-324008,-70879632] |
[a1,a2,a3,a4,a6] |
Generators |
[11971983:288442344:12167] |
Generators of the group modulo torsion |
j |
-918400908622515625/788493312 |
j-invariant |
L |
4.7938584922841 |
L(r)(E,1)/r! |
Ω |
0.10005308673716 |
Real period |
R |
11.978287349098 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997426 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9006d1 |
Quadratic twists by: -4 |