Atkin-Lehner |
2- 3+ 5- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69300o |
Isogeny class |
Conductor |
69300 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
31749120 |
Modular degree for the optimal curve |
Δ |
-1.7409501834982E+24 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7+ 11+ -4 -5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4604973000,-120278722387500] |
[a1,a2,a3,a4,a6] |
Generators |
[1180097478899744757364066443685984940452231443719251605346883469255013422826578827411475:31017247744345969377937210308753256844647218960609658610204879777141811896865465553090125:15001411767363837279587908229629903636803228283762823345541196095707097257442137831] |
Generators of the group modulo torsion |
j |
-799965408846201776676864/128959272851717 |
j-invariant |
L |
4.9431261477829 |
L(r)(E,1)/r! |
Ω |
0.0091635295097731 |
Real period |
R |
134.85868470525 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69300r1 69300u1 |
Quadratic twists by: -3 5 |