Atkin-Lehner |
3- 5+ 7- 11- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
42735k |
Isogeny class |
Conductor |
42735 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
453120 |
Modular degree for the optimal curve |
Δ |
-185373495849609375 = -1 · 3 · 512 · 75 · 11 · 372 |
Discriminant |
Eigenvalues |
1 3- 5+ 7- 11- -2 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-181154,-36206569] |
[a1,a2,a3,a4,a6] |
j |
-657451998475484928409/185373495849609375 |
j-invariant |
L |
2.2807806575503 |
L(r)(E,1)/r! |
Ω |
0.11403903288289 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128205bf1 |
Quadratic twists by: -3 |