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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 277725.cf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277725.cf1 | 277725cf1 | \([1, 1, 0, -238325, -43446000]\) | \(5177717/189\) | \(54646060587890625\) | \([2]\) | \(3041280\) | \(1.9812\) | \(\Gamma_0(N)\)-optimal |
277725.cf2 | 277725cf2 | \([1, 1, 0, 92300, -154205375]\) | \(300763/35721\) | \(-10328105451111328125\) | \([2]\) | \(6082560\) | \(2.3278\) |
Rank
sage: E.rank()
The elliptic curves in class 277725.cf have rank \(1\).
Complex multiplication
The elliptic curves in class 277725.cf do not have complex multiplication.Modular form 277725.2.a.cf
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.