Atkin-Lehner |
2+ 7- 17+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
68306h |
Isogeny class |
Conductor |
68306 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-731725929662630336 = -1 · 26 · 77 · 173 · 414 |
Discriminant |
Eigenvalues |
2+ 0 -2 7- -2 0 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-184543,51279885] |
[a1,a2,a3,a4,a6] |
Generators |
[-243:9162:1] |
Generators of the group modulo torsion |
j |
-5907850882757433/6219567779264 |
j-invariant |
L |
2.704966181167 |
L(r)(E,1)/r! |
Ω |
0.25910561751315 |
Real period |
R |
1.3049534619729 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000164 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9758f1 |
Quadratic twists by: -7 |