Atkin-Lehner |
2- 3+ 5- 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
129360ft |
Isogeny class |
Conductor |
129360 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
451584 |
Modular degree for the optimal curve |
Δ |
-284764105589040 = -1 · 24 · 36 · 5 · 79 · 112 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7- 11- -6 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-33385,2495452] |
[a1,a2,a3,a4,a6] |
Generators |
[-168:1826:1] |
Generators of the group modulo torsion |
j |
-6373654528/441045 |
j-invariant |
L |
4.8318309015166 |
L(r)(E,1)/r! |
Ω |
0.53905481925948 |
Real period |
R |
4.4817620491201 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000080325 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32340bm1 129360gy1 |
Quadratic twists by: -4 -7 |