Atkin-Lehner |
2+ 3- 7+ 11+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
13398k |
Isogeny class |
Conductor |
13398 |
Conductor |
∏ cp |
66 |
Product of Tamagawa factors cp |
deg |
813120 |
Modular degree for the optimal curve |
Δ |
-8.9301427120553E+19 |
Discriminant |
Eigenvalues |
2+ 3- -3 7+ 11+ 3 -5 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-4852585,-4139861140] |
[a1,a2,a3,a4,a6] |
Generators |
[16699:2129762:1] |
Generators of the group modulo torsion |
j |
-12636972422351146006413193/89301427120553066496 |
j-invariant |
L |
3.0263941706504 |
L(r)(E,1)/r! |
Ω |
0.050838527015147 |
Real period |
R |
0.90196274013612 |
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 |
107184cc1 40194bq1 93786m1 |
Quadratic twists by: -4 -3 -7 |