Properties

Label 61347.u
Number of curves 4
Conductor 61347
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("61347.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61347.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.u1 61347k4 [1, 1, 0, -1421631, 651813804] [2] 860160  
61347.u2 61347k3 [1, 1, 0, -399181, -88071914] [2] 860160  
61347.u3 61347k2 [1, 1, 0, -92446, 9285775] [2, 2] 430080  
61347.u4 61347k1 [1, 1, 0, 9799, 799440] [2] 215040 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 61347.u have rank \(0\).

Modular form 61347.2.a.u

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - 2q^{5} - q^{6} - 4q^{7} - 3q^{8} + q^{9} - 2q^{10} + q^{12} - 4q^{14} + 2q^{15} - q^{16} - 2q^{17} + q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.