Atkin-Lehner |
3- 11- 13- 53- |
Signs for the Atkin-Lehner involutions |
Class |
68211h |
Isogeny class |
Conductor |
68211 |
Conductor |
∏ cp |
70 |
Product of Tamagawa factors cp |
deg |
2815680 |
Modular degree for the optimal curve |
Δ |
-2.1042775780771E+20 |
Discriminant |
Eigenvalues |
-2 3- 2 -1 11- 13- 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-1408449,949223016] |
[a1,a2,a3,a4,a6] |
Generators |
[3548:201532:1] |
Generators of the group modulo torsion |
j |
-423857196397779300352/288652617020172691 |
j-invariant |
L |
3.8438858456788 |
L(r)(E,1)/r! |
Ω |
0.16401223357055 |
Real period |
R |
0.33480828679683 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000508 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7579a1 |
Quadratic twists by: -3 |