Atkin-Lehner |
3+ 5+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
9405a |
Isogeny class |
Conductor |
9405 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
77568 |
Modular degree for the optimal curve |
Δ |
-1606932421875 = -1 · 39 · 58 · 11 · 19 |
Discriminant |
Eigenvalues |
2 3+ 5+ 4 11+ -3 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-399303,-97118521] |
[a1,a2,a3,a4,a6] |
Generators |
[5774850041225694:1079831385559711247:165107731256] |
Generators of the group modulo torsion |
j |
-357717460495822848/81640625 |
j-invariant |
L |
8.6702600936366 |
L(r)(E,1)/r! |
Ω |
0.094960700534538 |
Real period |
R |
22.825916523444 |
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 |
9405d1 47025a1 103455d1 |
Quadratic twists by: -3 5 -11 |