Atkin-Lehner |
2+ 3+ 11+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
48312a |
Isogeny class |
Conductor |
48312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
43776 |
Modular degree for the optimal curve |
Δ |
-408139776 = -1 · 211 · 33 · 112 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ -3 2 11+ 0 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-11859,-497074] |
[a1,a2,a3,a4,a6] |
Generators |
[662:16786:1] |
Generators of the group modulo torsion |
j |
-3335601825558/7381 |
j-invariant |
L |
4.9291084950176 |
L(r)(E,1)/r! |
Ω |
0.2287480940058 |
Real period |
R |
5.3870487057237 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96624d1 48312j1 |
Quadratic twists by: -4 -3 |