Properties

Label 4400f
Number of curves 22
Conductor 44004400
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 4400f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4400.bb2 4400f1 [0,1,0,292,2912][0, -1, 0, 292, 2912] 5488/115488/11 5500000000-5500000000 [2][2] 32003200 0.553460.55346 Γ0(N)\Gamma_0(N)-optimal
4400.bb1 4400f2 [0,1,0,2208,32912][0, -1, 0, -2208, 32912] 595508/121595508/121 242000000000242000000000 [2][2] 64006400 0.900030.90003  

Rank

sage: E.rank()
 

The elliptic curves in class 4400f have rank 00.

Complex multiplication

The elliptic curves in class 4400f do not have complex multiplication.

Modular form 4400.2.a.f

sage: E.q_eigenform(10)
 
q+2q3+4q7+q9q11+6q132q174q19+O(q20)q + 2 q^{3} + 4 q^{7} + q^{9} - q^{11} + 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.