Atkin-Lehner |
2- 3+ 5- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
69600bk |
Isogeny class |
Conductor |
69600 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
180018257625000000 = 26 · 310 · 59 · 293 |
Discriminant |
Eigenvalues |
2- 3+ 5- -2 0 2 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-995958,-381692088] |
[a1,a2,a3,a4,a6] |
Generators |
[-110052403236:-139839043788:192100033] |
Generators of the group modulo torsion |
j |
874051874260928/1440146061 |
j-invariant |
L |
4.5747863309248 |
L(r)(E,1)/r! |
Ω |
0.15114098263606 |
Real period |
R |
15.134168943054 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000127 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69600by1 69600y1 |
Quadratic twists by: -4 5 |