Properties

Label 2112.j
Number of curves 4
Conductor 2112
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2112.j1")
sage: E.isogeny_class()

Elliptic curves in class 2112.j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
2112.j1 2112v3 [0, -1, 0, -9377, -346047] 2 3072  
2112.j2 2112v2 [0, -1, 0, -737, -2175] 4 1536  
2112.j3 2112v1 [0, -1, 0, -417, 3393] 2 768 \(\Gamma_0(N)\)-optimal
2112.j4 2112v4 [0, -1, 0, 2783, -19775] 2 3072  

Rank

sage: E.rank()

The elliptic curves in class 2112.j have rank \(1\).

Modular form 2112.2.a.j

sage: E.q_eigenform(10)
\( q - q^{3} + 2q^{5} - 4q^{7} + q^{9} + q^{11} + 2q^{13} - 2q^{15} - 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.