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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 272322c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272322.c1 | 272322c1 | \([1, -1, 0, -10401, 448433]\) | \(-35937/4\) | \(-13851303966756\) | \([]\) | \(829440\) | \(1.2590\) | \(\Gamma_0(N)\)-optimal |
272322.c2 | 272322c2 | \([1, -1, 0, 65244, -655984]\) | \(109503/64\) | \(-17951289940915776\) | \([]\) | \(2488320\) | \(1.8083\) |
Rank
sage: E.rank()
The elliptic curves in class 272322c have rank \(1\).
Complex multiplication
The elliptic curves in class 272322c do not have complex multiplication.Modular form 272322.2.a.c
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.