Atkin-Lehner |
2+ 3+ 23+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
78384b |
Isogeny class |
Conductor |
78384 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
26880 |
Modular degree for the optimal curve |
Δ |
-11287296 = -1 · 28 · 33 · 23 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ -3 0 -6 4 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-97,-371] |
[a1,a2,a3,a4,a6] |
Generators |
[12:7:1] |
Generators of the group modulo torsion |
j |
-398353408/44091 |
j-invariant |
L |
2.1607134381163 |
L(r)(E,1)/r! |
Ω |
0.75527158166217 |
Real period |
R |
2.8608430315706 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999850733 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39192j1 |
Quadratic twists by: -4 |