Atkin-Lehner |
2- 3+ 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112be |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
-1.5775080125769E+19 |
Discriminant |
Eigenvalues |
2- 3+ -1 -3 11+ -2 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-203283,-194321646] |
[a1,a2,a3,a4,a6] |
Generators |
[897:18576:1] |
Generators of the group modulo torsion |
j |
-11523267816003/195668237633 |
j-invariant |
L |
4.310770316233 |
L(r)(E,1)/r! |
Ω |
0.094831229492709 |
Real period |
R |
1.136432148816 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998664 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4257c1 68112bj1 |
Quadratic twists by: -4 -3 |