Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("ij1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120ij

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ix3 141120ij1 [0, 0, 0, -99372, -7611856] [2] 1179648 \(\Gamma_0(N)\)-optimal
141120.ix2 141120ij2 [0, 0, 0, -663852, 202600496] [2, 2] 2359296  
141120.ix1 141120ij3 [0, 0, 0, -10542252, 13174915376] [2] 4718592  
141120.ix4 141120ij4 [0, 0, 0, 182868, 683876144] [2] 4718592  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.ij

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

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.