Atkin-Lehner |
3+ 7- 17- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
77469j |
Isogeny class |
Conductor |
77469 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
5997600 |
Modular degree for the optimal curve |
Δ |
-8.6892924948943E+22 |
Discriminant |
Eigenvalues |
1 3+ 2 7- 1 4 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,9461091,8703185310] |
[a1,a2,a3,a4,a6] |
Generators |
[-988384607667111572182762:40490764906823993871835466:1284653000186515221731] |
Generators of the group modulo torsion |
j |
331563640418853143/307612526253381 |
j-invariant |
L |
8.1684243781286 |
L(r)(E,1)/r! |
Ω |
0.070438464975651 |
Real period |
R |
38.655131496464 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77469q1 |
Quadratic twists by: -7 |