Atkin-Lehner |
2- 3+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384cf |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
192512 |
Modular degree for the optimal curve |
Δ |
-13502206695744 = -1 · 26 · 316 · 132 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 2 -2 0 13- 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-28392,-1840410] |
[a1,a2,a3,a4,a6] |
Generators |
[60436468202037836790:-9153553292045734674213:2634361530731000] |
Generators of the group modulo torsion |
j |
-39550046044174912/210971979621 |
j-invariant |
L |
5.3904580954966 |
L(r)(E,1)/r! |
Ω |
0.18383608184236 |
Real period |
R |
29.322089777004 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999990022 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384dl1 36192bc2 |
Quadratic twists by: -4 8 |