Atkin-Lehner |
2- 3+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744bx |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
139776 |
Modular degree for the optimal curve |
Δ |
-779216621568 = -1 · 212 · 3 · 78 · 11 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 11- 6 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-36129,2655633] |
[a1,a2,a3,a4,a6] |
Generators |
[131:392:1] |
Generators of the group modulo torsion |
j |
-220881472/33 |
j-invariant |
L |
4.4776083301224 |
L(r)(E,1)/r! |
Ω |
0.86619023956877 |
Real period |
R |
0.86155214054988 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999532 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744ba1 103488cj1 51744co1 |
Quadratic twists by: -4 8 -7 |