Properties

Label 75150p
Number of curves 2
Conductor 75150
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("75150.y1")
sage: E.isogeny_class()

Elliptic curves in class 75150p

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
75150.y2 75150p1 [1, -1, 0, -1017, 52141] 2 147456 \(\Gamma_0(N)\)-optimal
75150.y1 75150p2 [1, -1, 0, -28017, 1807141] 2 294912  

Rank

sage: E.rank()

The elliptic curves in class 75150p have rank \(1\).

Modular form None

sage: E.q_eigenform(10)
\( q - q^{2} + q^{4} + 4q^{7} - q^{8} + 4q^{11} - 4q^{14} + q^{16} - 4q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.