Atkin-Lehner |
2- 7- 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
68432s |
Isogeny class |
Conductor |
68432 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
2027520 |
Modular degree for the optimal curve |
Δ |
-284494547681017856 = -1 · 220 · 7 · 132 · 475 |
Discriminant |
Eigenvalues |
2- -3 1 7- -1 13+ 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2789947,1793851498] |
[a1,a2,a3,a4,a6] |
Generators |
[-937:59878:1] [943:-1222:1] |
Generators of the group modulo torsion |
j |
-586342836493501890321/69456676679936 |
j-invariant |
L |
7.1757181392683 |
L(r)(E,1)/r! |
Ω |
0.29651428945812 |
Real period |
R |
1.2100121974561 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999737 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8554m1 |
Quadratic twists by: -4 |