Atkin-Lehner |
2- 3+ 5- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
51480bg |
Isogeny class |
Conductor |
51480 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3225600 |
Modular degree for the optimal curve |
Δ |
7113596901840 = 24 · 33 · 5 · 117 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 5- -4 11+ 13+ -4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-97435842,-370191316459] |
[a1,a2,a3,a4,a6] |
Generators |
[57460091789259082679312045695450:6402562812273953985940558667831977:3074514330767488295270795063] |
Generators of the group modulo torsion |
j |
236807903430715307255728128/16466659495 |
j-invariant |
L |
4.9927547146027 |
L(r)(E,1)/r! |
Ω |
0.048052929489154 |
Real period |
R |
51.950575830231 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000041 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
102960p1 51480e1 |
Quadratic twists by: -4 -3 |