Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48672x |
Isogeny class |
Conductor |
48672 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
599040 |
Modular degree for the optimal curve |
Δ |
-65765489792790528 = -1 · 212 · 39 · 138 |
Discriminant |
Eigenvalues |
2+ 3- -4 -3 2 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,52728,-11424400] |
[a1,a2,a3,a4,a6] |
Generators |
[676:18252:1] [932:29108:1] |
Generators of the group modulo torsion |
j |
6656/27 |
j-invariant |
L |
7.0437975490909 |
L(r)(E,1)/r! |
Ω |
0.17651053954055 |
Real period |
R |
1.6627424362841 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999988 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48672bz1 97344cv1 16224q1 48672by1 |
Quadratic twists by: -4 8 -3 13 |