Properties

Label 61347.v
Number of curves 2
Conductor 61347
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("61347.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61347.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.v1 61347i2 [1, 1, 0, -9077, 1847058] [] 235200  
61347.v2 61347i1 [1, 1, 0, -1212, -16947] [] 33600 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 61347.2.a.v

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} + 2q^{7} - 3q^{8} + q^{9} + q^{10} + q^{12} + 2q^{14} - q^{15} - q^{16} + 7q^{17} + q^{18} - 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.