Atkin-Lehner |
2+ 3+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
65472a |
Isogeny class |
Conductor |
65472 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
13104205153763328 = 216 · 39 · 11 · 314 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -2 11+ -4 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-278433,-56187999] |
[a1,a2,a3,a4,a6] |
Generators |
[3257761:-34843904:4913] |
Generators of the group modulo torsion |
j |
36425662686062500/199954302273 |
j-invariant |
L |
4.4939892254657 |
L(r)(E,1)/r! |
Ω |
0.2079039727192 |
Real period |
R |
10.807848370639 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996897 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
65472cr1 8184m1 |
Quadratic twists by: -4 8 |