Properties

Label 10920o
Number of curves $4$
Conductor $10920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10920o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10920.n4 10920o1 \([0, 1, 0, -6391, 79034]\) \(1804588288006144/866455078125\) \(13863281250000\) \([2]\) \(21504\) \(1.2155\) \(\Gamma_0(N)\)-optimal
10920.n2 10920o2 \([0, 1, 0, -84516, 9422784]\) \(260798860029250384/196803140625\) \(50381604000000\) \([2, 2]\) \(43008\) \(1.5620\)  
10920.n1 10920o3 \([0, 1, 0, -1352016, 604640784]\) \(266912903848829942596/152163375\) \(155815296000\) \([2]\) \(86016\) \(1.9086\)  
10920.n3 10920o4 \([0, 1, 0, -67016, 13454784]\) \(-32506165579682596/57814914850875\) \(-59202472807296000\) \([2]\) \(86016\) \(1.9086\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10920o have rank \(1\).

Complex multiplication

The elliptic curves in class 10920o do not have complex multiplication.

Modular form 10920.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} + 4q^{11} - q^{13} - q^{15} - 2q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.