Atkin-Lehner |
2+ 3- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
81312p |
Isogeny class |
Conductor |
81312 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
46080 |
Modular degree for the optimal curve |
Δ |
112698432 = 26 · 33 · 72 · 113 |
Discriminant |
Eigenvalues |
2+ 3- 0 7+ 11+ -2 -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4858,128720] |
[a1,a2,a3,a4,a6] |
Generators |
[41:-12:1] [-10:420:1] |
Generators of the group modulo torsion |
j |
148877000000/1323 |
j-invariant |
L |
12.472156791376 |
L(r)(E,1)/r! |
Ω |
1.6872440097281 |
Real period |
R |
1.2320048473272 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997775 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81312bc1 81312bs1 |
Quadratic twists by: -4 -11 |