Atkin-Lehner |
3+ 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
98397o |
Isogeny class |
Conductor |
98397 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1224960 |
Modular degree for the optimal curve |
Δ |
-2282624382341043 = -1 · 33 · 132 · 298 |
Discriminant |
Eigenvalues |
2 3+ -4 -3 -2 13- -2 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-73167,7956911] |
[a1,a2,a3,a4,a6] |
Generators |
[1682:10929:8] |
Generators of the group modulo torsion |
j |
-3207168/169 |
j-invariant |
L |
5.0785204839061 |
L(r)(E,1)/r! |
Ω |
0.45547199791487 |
Real period |
R |
0.92916807509386 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000018048 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
98397p1 98397n1 |
Quadratic twists by: -3 29 |