Properties

Label 9600.cd
Number of curves 22
Conductor 96009600
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 9600.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9600.cd1 9600v2 [0,1,0,633,4137][0, 1, 0, -633, -4137] 219488/75219488/75 96000000009600000000 [2][2] 92169216 0.617440.61744  
9600.cd2 9600v1 [0,1,0,117,387][0, 1, 0, 117, -387] 43904/4543904/45 180000000-180000000 [2][2] 46084608 0.270860.27086 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9600.cd have rank 00.

Complex multiplication

The elliptic curves in class 9600.cd do not have complex multiplication.

Modular form 9600.2.a.cd

sage: E.q_eigenform(10)
 
q+q3+4q7+q9+6q11+4q134q178q19+O(q20)q + q^{3} + 4 q^{7} + q^{9} + 6 q^{11} + 4 q^{13} - 4 q^{17} - 8 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 LMFDB 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 LMFDB labels.