Properties

Label 141120d
Number of curves $4$
Conductor $141120$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("141120.ir1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.ir4 141120d1 [0, 0, 0, 65268, 10224144] [2] 1179648 \(\Gamma_0(N)\)-optimal
141120.ir3 141120d2 [0, 0, 0, -499212, 109798416] [2, 2] 2359296  
141120.ir1 141120d3 [0, 0, 0, -7555212, 7992761616] [2] 4718592  
141120.ir2 141120d4 [0, 0, 0, -2474892, -1400411376] [2] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 141120d have rank \(1\).

Modular form 141120.2.a.ir

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

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.