Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("61347.w1")
sage: E.isogeny_class()

Elliptic curves in class 61347.w

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
61347.w1 61347j4 [1, 1, 0, -2996204, -1995493287] 2 1658880  
61347.w2 61347j2 [1, 1, 0, -235589, -13923840] 4 829440  
61347.w3 61347j1 [1, 1, 0, -133344, 18528723] 2 414720 \(\Gamma_0(N)\)-optimal
61347.w4 61347j3 [1, 1, 0, 889106, -107273525] 2 1658880  

Rank

sage: E.rank()

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

Modular form 61347.2.a.w

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.