Atkin-Lehner |
2+ 3+ 5+ 7- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
45150k |
Isogeny class |
Conductor |
45150 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
774144 |
Modular degree for the optimal curve |
Δ |
-278872248375000000 = -1 · 26 · 32 · 59 · 78 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7- 0 -4 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-477400,129280000] |
[a1,a2,a3,a4,a6] |
Generators |
[-4930:112715:8] [-275:15625:1] |
Generators of the group modulo torsion |
j |
-770109270718854529/17847823896000 |
j-invariant |
L |
6.208001942857 |
L(r)(E,1)/r! |
Ω |
0.30857238213501 |
Real period |
R |
0.6287019576153 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9030t1 |
Quadratic twists by: 5 |