Atkin-Lehner |
2- 3+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
77616da |
Isogeny class |
Conductor |
77616 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1244160 |
Modular degree for the optimal curve |
Δ |
-180952208769024 = -1 · 221 · 33 · 74 · 113 |
Discriminant |
Eigenvalues |
2- 3+ 3 7+ 11- 2 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5279211,-4668761062] |
[a1,a2,a3,a4,a6] |
Generators |
[1898035949:68576788566:571787] |
Generators of the group modulo torsion |
j |
-61279455929796531/681472 |
j-invariant |
L |
8.6295423727305 |
L(r)(E,1)/r! |
Ω |
0.049799766179196 |
Real period |
R |
14.440399748362 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000811 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9702bc1 77616cv2 77616ea1 |
Quadratic twists by: -4 -3 -7 |