Properties

Label 52371.e
Number of curves 2
Conductor 52371
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("52371.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 52371.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52371.e1 52371c2 [1, -1, 0, -5894217, -5463595706] [2] 1351680  
52371.e2 52371c1 [1, -1, 0, -109602, -203066825] [2] 675840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 52371.e have rank \(0\).

Modular form 52371.2.a.e

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} + 2q^{7} - 3q^{8} + q^{11} + 2q^{13} + 2q^{14} - q^{16} - 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.