Atkin-Lehner |
2- 5+ 11+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
53680t |
Isogeny class |
Conductor |
53680 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1624320 |
Modular degree for the optimal curve |
Δ |
-40954589843750000 = -1 · 24 · 518 · 11 · 61 |
Discriminant |
Eigenvalues |
2- 3 5+ 1 11+ 2 -5 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-5186773,-4546686097] |
[a1,a2,a3,a4,a6] |
Generators |
[221754046947428896788146007566290768682160018234292816971995868880467921066:644650860979317742584771561922126969898062880217458408705456694776716796875:84204058561483007710305388584554319019071382398177657003610630455626679] |
Generators of the group modulo torsion |
j |
-964484946807151601090304/2559661865234375 |
j-invariant |
L |
10.995735232068 |
L(r)(E,1)/r! |
Ω |
0.050020171854007 |
Real period |
R |
109.91300933713 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13420f1 |
Quadratic twists by: -4 |