Atkin-Lehner |
3+ 7- 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
69531d |
Isogeny class |
Conductor |
69531 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
56448 |
Modular degree for the optimal curve |
Δ |
-123178407891 = -1 · 3 · 72 · 117 · 43 |
Discriminant |
Eigenvalues |
0 3+ -2 7- 11+ -4 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,131,-16920] |
[a1,a2,a3,a4,a6] |
Generators |
[30:114:1] [44:268:1] |
Generators of the group modulo torsion |
j |
5035261952/2513845059 |
j-invariant |
L |
6.0357262391105 |
L(r)(E,1)/r! |
Ω |
0.48925227837081 |
Real period |
R |
12.336633892031 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69531h1 |
Quadratic twists by: -7 |