Atkin-Lehner |
3+ 17+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
85731a |
Isogeny class |
Conductor |
85731 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3709440 |
Modular degree for the optimal curve |
Δ |
6277746851855013033 = 38 · 173 · 417 |
Discriminant |
Eigenvalues |
1 3+ 2 -4 0 6 17+ -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-7008964,-7144051997] |
[a1,a2,a3,a4,a6] |
Generators |
[8373894041130812256505815968904266034848759624:-227503437502726106019235666918157314691468883007:2466810872278788346564395625565107352297984] |
Generators of the group modulo torsion |
j |
8016451263971353/1321601913 |
j-invariant |
L |
6.278508205644 |
L(r)(E,1)/r! |
Ω |
0.092787694863686 |
Real period |
R |
67.665310784116 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999932324 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2091b1 |
Quadratic twists by: 41 |