Properties

Label 51714.v
Number of curves $4$
Conductor $51714$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("51714.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51714.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
51714.v1 51714s4 [1, -1, 1, -171905, 19000271] [2] 663552  
51714.v2 51714s3 [1, -1, 1, -156695, 23910059] [2] 331776  
51714.v3 51714s2 [1, -1, 1, -65435, -6424765] [2] 221184  
51714.v4 51714s1 [1, -1, 1, -4595, -73069] [2] 110592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 51714.v have rank \(0\).

Modular form 51714.2.a.v

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 4q^{7} + q^{8} + 6q^{11} + 4q^{14} + q^{16} + q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.