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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 273600z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
273600.z2 | 273600z1 | \([0, 0, 0, -48300, -4082000]\) | \(450714348/475\) | \(13132800000000\) | \([2]\) | \(983040\) | \(1.4341\) | \(\Gamma_0(N)\)-optimal |
273600.z1 | 273600z2 | \([0, 0, 0, -60300, -1898000]\) | \(438512454/225625\) | \(12476160000000000\) | \([2]\) | \(1966080\) | \(1.7807\) |
Rank
sage: E.rank()
The elliptic curves in class 273600z have rank \(2\).
Complex multiplication
The elliptic curves in class 273600z do not have complex multiplication.Modular form 273600.2.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.