Atkin-Lehner |
2+ 5+ 13- 79+ |
Signs for the Atkin-Lehner involutions |
Class |
51350d |
Isogeny class |
Conductor |
51350 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
602112 |
Modular degree for the optimal curve |
Δ |
-14440441600000000 = -1 · 214 · 58 · 134 · 79 |
Discriminant |
Eigenvalues |
2+ 0 5+ -2 0 13- 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-901292,329617616] |
[a1,a2,a3,a4,a6] |
Generators |
[-251:23363:1] [529:-1077:1] |
Generators of the group modulo torsion |
j |
-5182036955574874641/924188262400 |
j-invariant |
L |
6.7409672764071 |
L(r)(E,1)/r! |
Ω |
0.38321344266873 |
Real period |
R |
2.1988292051625 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10270e1 |
Quadratic twists by: 5 |