Properties

Label 92400cx
Number of curves $2$
Conductor $92400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.gi2 92400cx1 \([0, 1, 0, -131348, -18305892]\) \(7831544736466064/29831377653\) \(954604084896000\) \([2]\) \(571392\) \(1.7332\) \(\Gamma_0(N)\)-optimal
92400.gi1 92400cx2 \([0, 1, 0, -2099648, -1171729692]\) \(7997484869919944276/116700507\) \(14937664896000\) \([2]\) \(1142784\) \(2.0797\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400cx have rank \(0\).

Complex multiplication

The elliptic curves in class 92400cx do not have complex multiplication.

Modular form 92400.2.a.cx

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + q^{11} + 4 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.