Atkin-Lehner |
2+ 3+ 5- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
33120c |
Isogeny class |
Conductor |
33120 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
24840000 = 26 · 33 · 54 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 -4 -2 -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-117,424] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:10:1] [-7:30:1] |
Generators of the group modulo torsion |
j |
102503232/14375 |
j-invariant |
L |
8.4207148629739 |
L(r)(E,1)/r! |
Ω |
2.042019442952 |
Real period |
R |
1.0309298097086 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999989 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
33120e1 66240di2 33120y1 |
Quadratic twists by: -4 8 -3 |