Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("61347.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61347l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.g2 61347l1 [1, 1, 1, 40472, -3939616] [2] 322560 \(\Gamma_0(N)\)-optimal
61347.g1 61347l2 [1, 1, 1, -266263, -39888958] [2] 645120  

Rank

sage: E.rank()
 

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

Modular form 61347.2.a.g

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.