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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 127600z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127600.j1 | 127600z1 | \([0, 1, 0, -21900033, -39454417562]\) | \(4646415367355940880384/38478378125\) | \(9619594531250000\) | \([2]\) | \(4515840\) | \(2.6547\) | \(\Gamma_0(N)\)-optimal |
127600.j2 | 127600z2 | \([0, 1, 0, -21884908, -39511620312]\) | \(-289799689905740628304/835751962890625\) | \(-3343007851562500000000\) | \([2]\) | \(9031680\) | \(3.0013\) |
Rank
sage: E.rank()
The elliptic curves in class 127600z have rank \(1\).
Complex multiplication
The elliptic curves in class 127600z do not have complex multiplication.Modular form 127600.2.a.z
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.