Atkin-Lehner |
2+ 3+ 5+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
129360d |
Isogeny class |
Conductor |
129360 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
191743860000000 = 28 · 3 · 57 · 74 · 113 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ 11- -1 8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-14961,233661] |
[a1,a2,a3,a4,a6] |
j |
602563032064/311953125 |
j-invariant |
L |
1.4968759333797 |
L(r)(E,1)/r! |
Ω |
0.49895861124096 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64680cj1 129360cz1 |
Quadratic twists by: -4 -7 |