Atkin-Lehner |
2- 3- 5+ 11- 31- |
Signs for the Atkin-Lehner involutions |
Class |
51150cq |
Isogeny class |
Conductor |
51150 |
Conductor |
∏ cp |
440 |
Product of Tamagawa factors cp |
deg |
1013760 |
Modular degree for the optimal curve |
Δ |
29961934992000000 = 210 · 311 · 56 · 11 · 312 |
Discriminant |
Eigenvalues |
2- 3- 5+ -4 11- 2 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1006638,388565892] |
[a1,a2,a3,a4,a6] |
Generators |
[696:-5370:1] |
Generators of the group modulo torsion |
j |
7219775199978393625/1917563839488 |
j-invariant |
L |
10.317032079685 |
L(r)(E,1)/r! |
Ω |
0.36321616125617 |
Real period |
R |
0.25822419465095 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999813 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2046b1 |
Quadratic twists by: 5 |