Atkin-Lehner |
2- 5+ 19+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
69350f |
Isogeny class |
Conductor |
69350 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
149760 |
Modular degree for the optimal curve |
Δ |
1647062500000 = 25 · 59 · 192 · 73 |
Discriminant |
Eigenvalues |
2- 1 5+ -3 -5 0 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-11563,473617] |
[a1,a2,a3,a4,a6] |
Generators |
[42:-271:1] [36:305:1] |
Generators of the group modulo torsion |
j |
10942526586601/105412000 |
j-invariant |
L |
15.68157941864 |
L(r)(E,1)/r! |
Ω |
0.84630343433905 |
Real period |
R |
0.46323749799294 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999985 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13870c1 |
Quadratic twists by: 5 |