Atkin-Lehner |
2+ 7- 11- 79+ |
Signs for the Atkin-Lehner involutions |
Class |
85162o |
Isogeny class |
Conductor |
85162 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2304000 |
Modular degree for the optimal curve |
Δ |
-2745316147318207232 = -1 · 28 · 711 · 11 · 793 |
Discriminant |
Eigenvalues |
2+ 1 4 7- 11- 1 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-669709,225453064] |
[a1,a2,a3,a4,a6] |
Generators |
[29095:1118662:125] |
Generators of the group modulo torsion |
j |
-282353350636276921/23334802227968 |
j-invariant |
L |
7.9208856356346 |
L(r)(E,1)/r! |
Ω |
0.25007215942662 |
Real period |
R |
3.9593000140384 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001272 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12166e1 |
Quadratic twists by: -7 |