Atkin-Lehner |
2+ 3+ 5+ 17- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
42330b |
Isogeny class |
Conductor |
42330 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
12184436520000 = 26 · 32 · 54 · 173 · 832 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 2 -4 -2 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-575963,168004317] |
[a1,a2,a3,a4,a6] |
Generators |
[446:-523:1] [-226:17045:1] |
Generators of the group modulo torsion |
j |
21130445120361306376249/12184436520000 |
j-invariant |
L |
5.8465541651771 |
L(r)(E,1)/r! |
Ω |
0.58676804551388 |
Real period |
R |
0.8303329583521 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
126990cc1 |
Quadratic twists by: -3 |