Atkin-Lehner |
2- 3+ 5- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
18240ca |
Isogeny class |
Conductor |
18240 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
16200683640000 = 26 · 310 · 54 · 193 |
Discriminant |
Eigenvalues |
2- 3+ 5- 0 2 -2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-7120,128782] |
[a1,a2,a3,a4,a6] |
Generators |
[99:620:1] |
Generators of the group modulo torsion |
j |
623799057208384/253135681875 |
j-invariant |
L |
4.5434498203374 |
L(r)(E,1)/r! |
Ω |
0.631574456431 |
Real period |
R |
3.5969233509001 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
18240cr1 9120f2 54720di1 91200hh1 |
Quadratic twists by: -4 8 -3 5 |