Properties

Label 54096.cz
Number of curves $4$
Conductor $54096$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 54096.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54096.cz1 54096cs4 \([0, 1, 0, -140217632, -639122076300]\) \(632678989847546725777/80515134\) \(38799462399860736\) \([2]\) \(4423680\) \(3.0431\)  
54096.cz2 54096cs3 \([0, 1, 0, -10026592, -6923474188]\) \(231331938231569617/90942310746882\) \(43824217772277434032128\) \([4]\) \(4423680\) \(3.0431\)  
54096.cz3 54096cs2 \([0, 1, 0, -8764352, -9986678220]\) \(154502321244119857/55101928644\) \(26553085145243467776\) \([2, 2]\) \(2211840\) \(2.6965\)  
54096.cz4 54096cs1 \([0, 1, 0, -469632, -202226508]\) \(-23771111713777/22848457968\) \(-11010450356130742272\) \([2]\) \(1105920\) \(2.3499\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54096.cz have rank \(0\).

Complex multiplication

The elliptic curves in class 54096.cz do not have complex multiplication.

Modular form 54096.2.a.cz

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2 q^{5} + q^{9} - 4 q^{11} - 2 q^{13} + 2 q^{15} - 6 q^{17} + O(q^{20})\) 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.