Atkin-Lehner |
2+ 3+ 19- 53- |
Signs for the Atkin-Lehner involutions |
Class |
48336m |
Isogeny class |
Conductor |
48336 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
267264 |
Modular degree for the optimal curve |
Δ |
-399495610801152 = -1 · 210 · 318 · 19 · 53 |
Discriminant |
Eigenvalues |
2+ 3+ 2 4 0 -4 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-52152,4701312] |
[a1,a2,a3,a4,a6] |
Generators |
[372:53900:27] |
Generators of the group modulo torsion |
j |
-15319513971103972/390132432423 |
j-invariant |
L |
6.9068611160448 |
L(r)(E,1)/r! |
Ω |
0.53201366782632 |
Real period |
R |
6.49124405417 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000022 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24168r1 |
Quadratic twists by: -4 |