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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 453152.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
453152.i1 | 453152i2 | \([0, 1, 0, -1024312, 397231260]\) | \(238328\) | \(498707442361028096\) | \([2]\) | \(8830976\) | \(2.2505\) | \(\Gamma_0(N)\)-optimal* |
453152.i2 | 453152i1 | \([0, 1, 0, -33042, 12221992]\) | \(-64\) | \(-62338430295128512\) | \([2]\) | \(4415488\) | \(1.9039\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 453152.i have rank \(1\).
Complex multiplication
The elliptic curves in class 453152.i do not have complex multiplication.Modular form 453152.2.a.i
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.