Atkin-Lehner |
2+ 31+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
85312f |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
107520 |
Modular degree for the optimal curve |
Δ |
323055386624 = 217 · 31 · 433 |
Discriminant |
Eigenvalues |
2+ -2 -3 2 -1 -1 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3457,72159] |
[a1,a2,a3,a4,a6] |
Generators |
[-30:387:1] [13:172:1] |
Generators of the group modulo torsion |
j |
34868843714/2464717 |
j-invariant |
L |
6.735423785121 |
L(r)(E,1)/r! |
Ω |
0.9457715073709 |
Real period |
R |
1.1869364027628 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000527 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85312u1 10664b1 |
Quadratic twists by: -4 8 |