Atkin-Lehner |
2- 3- 5+ 11- 31- |
Signs for the Atkin-Lehner involutions |
Class |
51150ck |
Isogeny class |
Conductor |
51150 |
Conductor |
∏ cp |
624 |
Product of Tamagawa factors cp |
deg |
958464 |
Modular degree for the optimal curve |
Δ |
-34651317888000000 = -1 · 213 · 38 · 56 · 113 · 31 |
Discriminant |
Eigenvalues |
2- 3- 5+ 1 11- 0 5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1475238,689605092] |
[a1,a2,a3,a4,a6] |
Generators |
[972:-13686:1] |
Generators of the group modulo torsion |
j |
-22724271869580547993/2217684344832 |
j-invariant |
L |
12.59417346681 |
L(r)(E,1)/r! |
Ω |
0.35194422679659 |
Real period |
R |
0.057347070253454 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999864 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2046c1 |
Quadratic twists by: 5 |