Atkin-Lehner |
3+ 5- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
5115c |
Isogeny class |
Conductor |
5115 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2048 |
Modular degree for the optimal curve |
Δ |
-457142895 = -1 · 32 · 5 · 11 · 314 |
Discriminant |
Eigenvalues |
-1 3+ 5- 0 11+ 6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-310,2210] |
[a1,a2,a3,a4,a6] |
Generators |
[4:30:1] |
Generators of the group modulo torsion |
j |
-3295310559841/457142895 |
j-invariant |
L |
2.2249658628769 |
L(r)(E,1)/r! |
Ω |
1.6133380638534 |
Real period |
R |
2.758214056591 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
81840dk1 15345h1 25575i1 56265j1 |
Quadratic twists by: -4 -3 5 -11 |