Atkin-Lehner |
2+ 7- 17- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
68306i |
Isogeny class |
Conductor |
68306 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
604800 |
Modular degree for the optimal curve |
Δ |
-22505558991596324 = -1 · 22 · 710 · 172 · 413 |
Discriminant |
Eigenvalues |
2+ -1 3 7- 3 4 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-51671,-8538263] |
[a1,a2,a3,a4,a6] |
Generators |
[37680:211319:125] |
Generators of the group modulo torsion |
j |
-54012843913/79672676 |
j-invariant |
L |
5.4098325949232 |
L(r)(E,1)/r! |
Ω |
0.15038551896946 |
Real period |
R |
8.993273807724 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994216 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68306b1 |
Quadratic twists by: -7 |