Atkin-Lehner |
2+ 3- 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
76608bi |
Isogeny class |
Conductor |
76608 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-1941100858368 = -1 · 210 · 37 · 74 · 192 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ -2 -2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-11136,457256] |
[a1,a2,a3,a4,a6] |
Generators |
[-74:936:1] [25:441:1] |
Generators of the group modulo torsion |
j |
-204589760512/2600283 |
j-invariant |
L |
9.0130580500564 |
L(r)(E,1)/r! |
Ω |
0.83390201999982 |
Real period |
R |
1.3510367276272 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999537 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
76608fr1 4788c1 25536a1 |
Quadratic twists by: -4 8 -3 |