Properties

Label 4840.f
Number of curves 4
Conductor 4840
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4840.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4840.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4840.f1 4840g3 [0, 0, 0, -12947, 567006] [2] 5120  
4840.f2 4840g2 [0, 0, 0, -847, 7986] [2, 2] 2560  
4840.f3 4840g1 [0, 0, 0, -242, -1331] [2] 1280 \(\Gamma_0(N)\)-optimal
4840.f4 4840g4 [0, 0, 0, 1573, 45254] [2] 5120  

Rank

sage: E.rank()
 

The elliptic curves in class 4840.f have rank \(0\).

Modular form 4840.2.a.f

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{7} - 3q^{9} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.