Atkin-Lehner |
2+ 3- 7- 61- |
Signs for the Atkin-Lehner involutions |
Class |
61488i |
Isogeny class |
Conductor |
61488 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
90624 |
Modular degree for the optimal curve |
Δ |
-93713614848 = -1 · 211 · 37 · 73 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- -5 -7 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-507,15370] |
[a1,a2,a3,a4,a6] |
Generators |
[41:-252:1] [-22:126:1] |
Generators of the group modulo torsion |
j |
-9653618/62769 |
j-invariant |
L |
7.5211620345824 |
L(r)(E,1)/r! |
Ω |
0.92153641916301 |
Real period |
R |
0.17003221192533 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000027 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
30744f1 20496g1 |
Quadratic twists by: -4 -3 |