Properties

Label 141120.fs
Number of curves $2$
Conductor $141120$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("141120.fs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120.fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.fs1 141120mh1 [0, 0, 0, -423948, -40605712] [2] 2064384 \(\Gamma_0(N)\)-optimal
141120.fs2 141120mh2 [0, 0, 0, 1551732, -311669008] [2] 4128768  

Rank

sage: E.rank()
 

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

Modular form 141120.2.a.fs

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.