Atkin-Lehner |
2+ 3- 47- |
Signs for the Atkin-Lehner involutions |
Class |
27072bi |
Isogeny class |
Conductor |
27072 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
135168 |
Modular degree for the optimal curve |
Δ |
99444124237824 = 214 · 317 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -3 -1 5 4 4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-164784,-25742176] |
[a1,a2,a3,a4,a6] |
Generators |
[-519155:94041:2197] |
Generators of the group modulo torsion |
j |
41430613746688/8325909 |
j-invariant |
L |
4.8323379632289 |
L(r)(E,1)/r! |
Ω |
0.236960540451 |
Real period |
R |
5.0982517532578 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27072cg1 3384f1 9024g1 |
Quadratic twists by: -4 8 -3 |