Atkin-Lehner |
2- 3+ 7+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
48048bg |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
14 |
Product of Tamagawa factors cp |
deg |
383040 |
Modular degree for the optimal curve |
Δ |
-300566400406272 = -1 · 28 · 35 · 7 · 11 · 137 |
Discriminant |
Eigenvalues |
2- 3+ 4 7+ 11+ 13- -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-110461,14192113] |
[a1,a2,a3,a4,a6] |
Generators |
[117:1690:1] |
Generators of the group modulo torsion |
j |
-582256828038897664/1174087501587 |
j-invariant |
L |
6.2856711382121 |
L(r)(E,1)/r! |
Ω |
0.54658190726082 |
Real period |
R |
0.82142585385352 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12012i1 |
Quadratic twists by: -4 |