Properties

Label 141120.ox
Number of curves $4$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ox1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.ox

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.ox1 141120kb3 \([0, 0, 0, -571564812, 5259522722384]\) \(7347751505995469192/72930375\) \(204962377460133888000\) \([2]\) \(23592960\) \(3.4737\)  
141120.ox2 141120kb4 \([0, 0, 0, -51184812, 4300358384]\) \(5276930158229192/3050936350875\) \(8574303477184715354112000\) \([2]\) \(23592960\) \(3.4737\)  
141120.ox3 141120kb2 \([0, 0, 0, -35749812, 82049540384]\) \(14383655824793536/45209390625\) \(15881969937121344000000\) \([2, 2]\) \(11796480\) \(3.1271\)  
141120.ox4 141120kb1 \([0, 0, 0, -1296687, 2366352884]\) \(-43927191786304/415283203125\) \(-2279502684703125000000\) \([2]\) \(5898240\) \(2.7806\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141120.ox have rank \(0\).

Complex multiplication

The elliptic curves in class 141120.ox do not have complex multiplication.

Modular form 141120.2.a.ox

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{11} - 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.