Properties

Label 30015.d
Number of curves 2
Conductor 30015
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("30015.d1")
sage: E.isogeny_class()

Elliptic curves in class 30015.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
30015.d1 30015m1 [1, -1, 1, -3362, -74176] 2 13824 \(\Gamma_0(N)\)-optimal
30015.d2 30015m2 [1, -1, 1, -3137, -84706] 2 27648  

Rank

sage: E.rank()

The elliptic curves in class 30015.d have rank \(0\).

Modular form 30015.2.a.d

sage: E.q_eigenform(10)
\( q - q^{2} - q^{4} + q^{5} + 3q^{8} - q^{10} - 2q^{11} + 2q^{13} - q^{16} + 4q^{17} + O(q^{20}) \)

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.