Properties

Label 786.m
Number of curves 2
Conductor 786
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("786.m1")
sage: E.isogeny_class()

Elliptic curves in class 786.m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
786.m1 786m2 [1, 0, 0, -227045, -41659377] 1 4200  
786.m2 786m1 [1, 0, 0, -2135, 35913] 5 840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 786.m have rank \(0\).

Modular form 786.2.a.m

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 3q^{7} + q^{8} + q^{9} + q^{10} - 3q^{11} + q^{12} + 4q^{13} + 3q^{14} + q^{15} + q^{16} - 7q^{17} + q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.