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SageMath
E = EllipticCurve("hi1")
E.isogeny_class()
Elliptic curves in class 485520.hi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.hi1 | 485520hi2 | \([0, 1, 0, -3360, 35508]\) | \(208527857/91875\) | \(1848860160000\) | \([2]\) | \(786432\) | \(1.0496\) | \(\Gamma_0(N)\)-optimal* |
485520.hi2 | 485520hi1 | \([0, 1, 0, 720, 4500]\) | \(2048383/1575\) | \(-31694745600\) | \([2]\) | \(393216\) | \(0.70303\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.hi have rank \(0\).
Complex multiplication
The elliptic curves in class 485520.hi do not have complex multiplication.Modular form 485520.2.a.hi
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.