Atkin-Lehner |
3- 7- 17+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72471j |
Isogeny class |
Conductor |
72471 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
-30537029354670783 = -1 · 37 · 78 · 174 · 29 |
Discriminant |
Eigenvalues |
-1 3- 0 7- 0 -2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,31702,8124675] |
[a1,a2,a3,a4,a6] |
Generators |
[139:-3971:1] |
Generators of the group modulo torsion |
j |
29949846491375/259560466767 |
j-invariant |
L |
4.5757046843084 |
L(r)(E,1)/r! |
Ω |
0.27181287688434 |
Real period |
R |
1.2024303358914 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000842 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10353a1 |
Quadratic twists by: -7 |