Atkin-Lehner |
2- 3+ 7- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
72324a |
Isogeny class |
Conductor |
72324 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
152064 |
Modular degree for the optimal curve |
Δ |
29304466574544 = 24 · 33 · 79 · 412 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 2 -4 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-18816,958685] |
[a1,a2,a3,a4,a6] |
Generators |
[-73:1394:1] |
Generators of the group modulo torsion |
j |
14495514624/576583 |
j-invariant |
L |
4.4059863658787 |
L(r)(E,1)/r! |
Ω |
0.65698086003375 |
Real period |
R |
3.353207555327 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999971354 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72324b1 10332b1 |
Quadratic twists by: -3 -7 |