Properties

Label 10470.d
Number of curves 2
Conductor 10470
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("10470.d1")
sage: E.isogeny_class()

Elliptic curves in class 10470.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10470.d1 10470d1 [1, 0, 0, -45435, 3726225] 7 38808 \(\Gamma_0(N)\)-optimal
10470.d2 10470d2 [1, 0, 0, 182415, -207095505] 1 271656  

Rank

sage: E.rank()

The elliptic curves in class 10470.d have rank \(0\).

Modular form 10470.2.a.d

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} + q^{14} + q^{15} + q^{16} - 3q^{17} + q^{18} + 6q^{19} + O(q^{20}) \)

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.