Properties

Label 52371.f
Number of curves 3
Conductor 52371
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("52371.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 52371.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52371.f1 52371f3 [0, 0, 1, -37232607, -87444657887] [] 1897500  
52371.f2 52371f2 [0, 0, 1, -49197, -7607417] [] 379500  
52371.f3 52371f1 [0, 0, 1, -1587, 57793] [] 75900 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 52371.2.a.f

sage: E.q_eigenform(10)
 
\( q + 2q^{2} + 2q^{4} + q^{5} + 2q^{7} + 2q^{10} + q^{11} + 4q^{13} + 4q^{14} - 4q^{16} - 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.