Properties

Label 2420.e
Number of curves 2
Conductor 2420
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2420.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2420.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2420.e1 2420d2 [0, 1, 0, -52796, -4688620] [] 4752  
2420.e2 2420d1 [0, 1, 0, 444, -24796] [3] 1584 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2420.e have rank \(1\).

Modular form 2420.2.a.e

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} - q^{7} - 2q^{9} + 2q^{13} - q^{15} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.