Atkin-Lehner |
2+ 3+ 31- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
34968b |
Isogeny class |
Conductor |
34968 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
-7188651504 = -1 · 24 · 38 · 31 · 472 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -3 0 -4 0 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-656,7869] |
[a1,a2,a3,a4,a6] |
Generators |
[10:-47:1] [2:81:1] |
Generators of the group modulo torsion |
j |
-1954236469504/449290719 |
j-invariant |
L |
6.5175412558872 |
L(r)(E,1)/r! |
Ω |
1.2648133727718 |
Real period |
R |
0.64412084385271 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69936f1 104904o1 |
Quadratic twists by: -4 -3 |