Atkin-Lehner |
5- 7- 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
83545f |
Isogeny class |
Conductor |
83545 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
460800 |
Modular degree for the optimal curve |
Δ |
-4309583974609375 = -1 · 510 · 76 · 112 · 31 |
Discriminant |
Eigenvalues |
1 2 5- 7- 11+ 4 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-47212,-5076021] |
[a1,a2,a3,a4,a6] |
Generators |
[31758:5643621:1] |
Generators of the group modulo torsion |
j |
-98925223576249/36630859375 |
j-invariant |
L |
12.228332869523 |
L(r)(E,1)/r! |
Ω |
0.1590013781778 |
Real period |
R |
3.8453543623446 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004602 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1705a1 |
Quadratic twists by: -7 |