Atkin-Lehner |
3+ 5- 31+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
28365b |
Isogeny class |
Conductor |
28365 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
-12068598375 = -1 · 33 · 53 · 312 · 612 |
Discriminant |
Eigenvalues |
-1 3+ 5- 0 -6 -4 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-560,7112] |
[a1,a2,a3,a4,a6] |
Generators |
[-28:56:1] [2:76:1] |
Generators of the group modulo torsion |
j |
-19423892355841/12068598375 |
j-invariant |
L |
4.6508259170085 |
L(r)(E,1)/r! |
Ω |
1.1739614594763 |
Real period |
R |
1.3205504262136 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85095h1 |
Quadratic twists by: -3 |