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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 453299j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
453299.j2 | 453299j1 | \([1, 1, 1, 143373, -79227856]\) | \(4657463/41503\) | \(-2904395250138330487\) | \([2]\) | \(6967296\) | \(2.2240\) | \(\Gamma_0(N)\)-optimal* |
453299.j1 | 453299j2 | \([1, 1, 1, -2123122, -1100057204]\) | \(15124197817/1294139\) | \(90564324617949759731\) | \([2]\) | \(13934592\) | \(2.5706\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 453299j have rank \(0\).
Complex multiplication
The elliptic curves in class 453299j do not have complex multiplication.Modular form 453299.2.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 Cremona 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 Cremona labels.