Atkin-Lehner |
2- 5- 13- 67- |
Signs for the Atkin-Lehner involutions |
Class |
69680bi |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
912 |
Product of Tamagawa factors cp |
deg |
88646400 |
Modular degree for the optimal curve |
Δ |
-2.14752301075E+28 |
Discriminant |
Eigenvalues |
2- 0 5- -3 -3 13- 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27104189867,1717538256339674] |
[a1,a2,a3,a4,a6] |
Generators |
[98933:2090400:1] |
Generators of the group modulo torsion |
j |
-537617079035035624542262006188801/5242976100463867187500000 |
j-invariant |
L |
5.0350152603255 |
L(r)(E,1)/r! |
Ω |
0.03454277574368 |
Real period |
R |
0.15982647447932 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000551 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8710k1 |
Quadratic twists by: -4 |