Atkin-Lehner |
2+ 3+ 5- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
34320g |
Isogeny class |
Conductor |
34320 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-71172105468750000 = -1 · 24 · 34 · 512 · 113 · 132 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 0 11- 13+ 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,28105,-12716118] |
[a1,a2,a3,a4,a6] |
Generators |
[4694:-321750:1] |
Generators of the group modulo torsion |
j |
153440161062692864/4448256591796875 |
j-invariant |
L |
5.3106715589696 |
L(r)(E,1)/r! |
Ω |
0.16711505992537 |
Real period |
R |
0.88273704644991 |
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 |
17160h1 102960s1 |
Quadratic twists by: -4 -3 |