Atkin-Lehner |
2- 3+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744bv |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
179712 |
Modular degree for the optimal curve |
Δ |
-172472994828288 = -1 · 212 · 313 · 74 · 11 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 11- -2 -1 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,10911,-458415] |
[a1,a2,a3,a4,a6] |
Generators |
[947:29296:1] |
Generators of the group modulo torsion |
j |
14605803968/17537553 |
j-invariant |
L |
3.8143883837112 |
L(r)(E,1)/r! |
Ω |
0.30686102456847 |
Real period |
R |
6.215172469563 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998729 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744y1 103488cg1 51744cl1 |
Quadratic twists by: -4 8 -7 |