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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 12936.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12936.a1 | 12936f1 | \([0, -1, 0, -392800, 94886716]\) | \(55635379958596/24057\) | \(2898208760832\) | \([2]\) | \(120960\) | \(1.7337\) | \(\Gamma_0(N)\)-optimal |
12936.a2 | 12936f2 | \([0, -1, 0, -390840, 95878476]\) | \(-27403349188178/578739249\) | \(-139444416318670848\) | \([2]\) | \(241920\) | \(2.0802\) |
Rank
sage: E.rank()
The elliptic curves in class 12936.a have rank \(0\).
Complex multiplication
The elliptic curves in class 12936.a do not have complex multiplication.Modular form 12936.2.a.a
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.