Atkin-Lehner |
2+ 3- 7+ 11- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
13398m |
Isogeny class |
Conductor |
13398 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
2652804 = 22 · 33 · 7 · 112 · 29 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 11- -2 4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-122,-520] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:4:1] |
Generators of the group modulo torsion |
j |
198461344537/2652804 |
j-invariant |
L |
3.3974677764086 |
L(r)(E,1)/r! |
Ω |
1.4390906919468 |
Real period |
R |
0.78694780331795 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
107184br1 40194bk1 93786o1 |
Quadratic twists by: -4 -3 -7 |