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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 485100cr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.cr2 | 485100cr1 | \([0, 0, 0, 2851800, 4640618500]\) | \(7476617216/31444875\) | \(-10787619816319500000000\) | \([]\) | \(23887872\) | \(2.9103\) | \(\Gamma_0(N)\)-optimal |
485100.cr1 | 485100cr2 | \([0, 0, 0, -26254200, -142257363500]\) | \(-5833703071744/22107421875\) | \(-7584271278117187500000000\) | \([]\) | \(71663616\) | \(3.4596\) |
Rank
sage: E.rank()
The elliptic curves in class 485100cr have rank \(0\).
Complex multiplication
The elliptic curves in class 485100cr do not have complex multiplication.Modular form 485100.2.a.cr
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.