Properties

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

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 141120cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.ov3 141120cb1 \([0, 0, 0, -99372, 7611856]\) \(4826809/1680\) \(37771564359352320\) \([2]\) \(1179648\) \(1.8824\) \(\Gamma_0(N)\)-optimal
141120.ov2 141120cb2 \([0, 0, 0, -663852, -202600496]\) \(1439069689/44100\) \(991503564432998400\) \([2, 2]\) \(2359296\) \(2.2290\)  
141120.ov4 141120cb3 \([0, 0, 0, 182868, -683876144]\) \(30080231/9003750\) \(-202431977738403840000\) \([2]\) \(4718592\) \(2.5756\)  
141120.ov1 141120cb4 \([0, 0, 0, -10542252, -13174915376]\) \(5763259856089/5670\) \(127479029712814080\) \([2]\) \(4718592\) \(2.5756\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.cb

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