Properties

Label 51870.h
Number of curves 2
Conductor 51870
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("51870.h1")
sage: E.isogeny_class()

Elliptic curves in class 51870.h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
51870.h1 51870f2 [1, 1, 0, -9718, -372812] 2 66560  
51870.h2 51870f1 [1, 1, 0, -598, -6188] 2 33280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 51870.h have rank \(0\).

Modular form None

sage: E.q_eigenform(10)
\( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{12} - q^{13} - q^{14} + q^{15} + q^{16} + 2q^{17} - q^{18} - q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.