Atkin-Lehner |
2- 3- 43+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
72756d |
Isogeny class |
Conductor |
72756 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
47040 |
Modular degree for the optimal curve |
Δ |
-51554028528 = -1 · 24 · 313 · 43 · 47 |
Discriminant |
Eigenvalues |
2- 3- -2 -2 -3 -2 0 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,699,-8291] |
[a1,a2,a3,a4,a6] |
Generators |
[35:-243:1] [20:117:1] |
Generators of the group modulo torsion |
j |
3238230272/4419927 |
j-invariant |
L |
8.755632283848 |
L(r)(E,1)/r! |
Ω |
0.59850766607664 |
Real period |
R |
1.2190921938233 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999953 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24252d1 |
Quadratic twists by: -3 |