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Properties

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

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

Elliptic curves in class 52371f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52371.f3 52371f1 \([0, 0, 1, -1587, 57793]\) \(-4096/11\) \(-1187099793891\) \([]\) \(75900\) \(1.0043\) \(\Gamma_0(N)\)-optimal
52371.f2 52371f2 \([0, 0, 1, -49197, -7607417]\) \(-122023936/161051\) \(-17380328082358131\) \([]\) \(379500\) \(1.8090\)  
52371.f1 52371f3 \([0, 0, 1, -37232607, -87444657887]\) \(-52893159101157376/11\) \(-1187099793891\) \([]\) \(1897500\) \(2.6138\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 52371f do not have complex multiplication.

Modular form 52371.2.a.f

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

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 Cremona 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 Cremona labels.