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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 485100.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.co1 | 485100co2 | \([0, 0, 0, -10367175, 4962266750]\) | \(1047213232/515625\) | \(60674170224937500000000\) | \([2]\) | \(30965760\) | \(3.0648\) | \(\Gamma_0(N)\)-optimal* |
485100.co2 | 485100co1 | \([0, 0, 0, 2366700, 594547625]\) | \(199344128/136125\) | \(-1001123808711468750000\) | \([2]\) | \(15482880\) | \(2.7183\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485100.co have rank \(0\).
Complex multiplication
The elliptic curves in class 485100.co do not have complex multiplication.Modular form 485100.2.a.co
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.