Atkin-Lehner |
2+ 3- 7- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
49728ci |
Isogeny class |
Conductor |
49728 |
Conductor |
∏ cp |
34 |
Product of Tamagawa factors cp |
deg |
261120 |
Modular degree for the optimal curve |
Δ |
-4384004796186624 = -1 · 217 · 317 · 7 · 37 |
Discriminant |
Eigenvalues |
2+ 3- 3 7- 0 2 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-63649,6932159] |
[a1,a2,a3,a4,a6] |
Generators |
[125:972:1] |
Generators of the group modulo torsion |
j |
-217568172289106/33447302217 |
j-invariant |
L |
10.033467563279 |
L(r)(E,1)/r! |
Ω |
0.42146162260912 |
Real period |
R |
0.70018709017297 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000034 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
49728cz1 6216h1 |
Quadratic twists by: -4 8 |