Atkin-Lehner |
2- 3+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744bt |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
207360 |
Modular degree for the optimal curve |
Δ |
-3180800544768 = -1 · 212 · 35 · 74 · 113 |
Discriminant |
Eigenvalues |
2- 3+ -4 7+ 11+ -4 -7 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-11825,-498399] |
[a1,a2,a3,a4,a6] |
j |
-18595667776/323433 |
j-invariant |
L |
0.91469834272206 |
L(r)(E,1)/r! |
Ω |
0.22867458571411 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744cg1 103488hg1 51744ck1 |
Quadratic twists by: -4 8 -7 |