Atkin-Lehner |
2+ 3+ 7- 23- |
Signs for the Atkin-Lehner involutions |
Class |
30912p |
Isogeny class |
Conductor |
30912 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
156672 |
Modular degree for the optimal curve |
Δ |
-1871817889148928 = -1 · 212 · 32 · 73 · 236 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- -4 -4 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-28329,-2765655] |
[a1,a2,a3,a4,a6] |
Generators |
[1263:44436:1] |
Generators of the group modulo torsion |
j |
-613864936718272/456986789343 |
j-invariant |
L |
3.2128115687522 |
L(r)(E,1)/r! |
Ω |
0.17821831544002 |
Real period |
R |
0.50076090988922 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
30912u1 15456f1 92736bz1 |
Quadratic twists by: -4 8 -3 |