Atkin-Lehner |
2+ 3+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384h |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-317827171740672 = -1 · 210 · 39 · 112 · 194 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 11- -2 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8640,-911736] |
[a1,a2,a3,a4,a6] |
Generators |
[153:1161:1] |
Generators of the group modulo torsion |
j |
-3538944000/15768841 |
j-invariant |
L |
6.7677160819618 |
L(r)(E,1)/r! |
Ω |
0.22478298342163 |
Real period |
R |
3.7634722051688 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993261 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
120384by1 7524a1 120384c1 |
Quadratic twists by: -4 8 -3 |