Properties

Label 121242.bp
Number of curves 2
Conductor 121242
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("121242.bp1")
sage: E.isogeny_class()

Elliptic curves in class 121242.bp

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
121242.bp1 121242bk2 [1, 0, 0, -15067, 708665] 2 368640  
121242.bp2 121242bk1 [1, 0, 0, -547, 20417] 2 184320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 121242.bp have rank \(0\).

Modular form 121242.2.a.bp

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

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 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.