Atkin-Lehner |
2+ 7- 29- 31- |
Signs for the Atkin-Lehner involutions |
Class |
12586d |
Isogeny class |
Conductor |
12586 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
10368 |
Modular degree for the optimal curve |
Δ |
148187564 = 22 · 72 · 293 · 31 |
Discriminant |
Eigenvalues |
2+ -2 -3 7- 0 -4 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-2440,46170] |
[a1,a2,a3,a4,a6] |
Generators |
[-57:57:1] [-28:318:1] |
Generators of the group modulo torsion |
j |
1605599802471673/148187564 |
j-invariant |
L |
3.1191283049226 |
L(r)(E,1)/r! |
Ω |
1.7513104464753 |
Real period |
R |
1.3357690142263 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999969 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
100688v1 113274bs1 88102f1 |
Quadratic twists by: -4 -3 -7 |