Properties

Label 54720.cj
Number of curves $4$
Conductor $54720$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 54720.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54720.cj1 54720bl4 \([0, 0, 0, -710463468, 7288854554288]\) \(207530301091125281552569/805586668007040\) \(153950009682069332951040\) \([2]\) \(13762560\) \(3.6624\)  
54720.cj2 54720bl3 \([0, 0, 0, -134647788, -464329726288]\) \(1412712966892699019449/330160465517040000\) \(63094647517851722711040000\) \([2]\) \(13762560\) \(3.6624\)  
54720.cj3 54720bl2 \([0, 0, 0, -45068268, 110304978608]\) \(52974743974734147769/3152005008998400\) \(602357537586501019238400\) \([2, 2]\) \(6881280\) \(3.3159\)  
54720.cj4 54720bl1 \([0, 0, 0, 2117652, 7118808752]\) \(5495662324535111/117739817533440\) \(-22500429524337363517440\) \([2]\) \(3440640\) \(2.9693\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54720.cj have rank \(1\).

Complex multiplication

The elliptic curves in class 54720.cj do not have complex multiplication.

Modular form 54720.2.a.cj

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{7} - 2 q^{13} + 2 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.