Atkin-Lehner |
2+ 3+ 5+ 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
111150b |
Isogeny class |
Conductor |
111150 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
235008 |
Modular degree for the optimal curve |
Δ |
-1504693125000 = -1 · 23 · 33 · 57 · 13 · 193 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -2 -3 13+ -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-7692,268216] |
[a1,a2,a3,a4,a6] |
Generators |
[-61:743:1] [29:248:1] |
Generators of the group modulo torsion |
j |
-119313478467/3566680 |
j-invariant |
L |
7.9585774031367 |
L(r)(E,1)/r! |
Ω |
0.8455333976857 |
Real period |
R |
0.39218721893429 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001295 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111150cx2 22230y1 |
Quadratic twists by: -3 5 |