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SageMath
sage: E = EllipticCurve("j1")
sage: E.isogeny_class()
Elliptic curves in class 1152.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
1152.j1 | 1152q1 | [0, 0, 0, -30, -52] | [2] | 128 | \(\Gamma_0(N)\)-optimal |
1152.j2 | 1152q2 | [0, 0, 0, 60, -304] | [2] | 256 |
Rank
sage: E.rank()
The elliptic curves in class 1152.j have rank \(1\).
Complex multiplication
The elliptic curves in class 1152.j do not have complex multiplication.Modular form 1152.2.a.j
sage: E.q_eigenform(10)
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.