Atkin-Lehner |
2- 3+ 7+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69384t |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
-20398896 = -1 · 24 · 32 · 74 · 59 |
Discriminant |
Eigenvalues |
2- 3+ -3 7+ -2 -2 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,33,-216] |
[a1,a2,a3,a4,a6] |
Generators |
[5:7:1] [9:27:1] |
Generators of the group modulo torsion |
j |
100352/531 |
j-invariant |
L |
7.3833336094992 |
L(r)(E,1)/r! |
Ω |
1.0848084772099 |
Real period |
R |
0.56717643134025 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69384be1 |
Quadratic twists by: -7 |