Atkin-Lehner |
7- 13+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
83993f |
Isogeny class |
Conductor |
83993 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
19392 |
Modular degree for the optimal curve |
Δ |
-41744521 = -1 · 72 · 132 · 712 |
Discriminant |
Eigenvalues |
-1 0 -3 7- -6 13+ 3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-19,-308] |
[a1,a2,a3,a4,a6] |
Generators |
[40:228:1] [19:67:1] |
Generators of the group modulo torsion |
j |
-4270617/247009 |
j-invariant |
L |
5.3039823807383 |
L(r)(E,1)/r! |
Ω |
0.8941249201885 |
Real period |
R |
1.4830093258754 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000358 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
83993c1 |
Quadratic twists by: 13 |