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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 272832n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272832.n2 | 272832n1 | \([0, -1, 0, -1154309, 477728469]\) | \(4116309458944/2523\) | \(104255642072064\) | \([2]\) | \(3268608\) | \(2.0113\) | \(\Gamma_0(N)\)-optimal |
272832.n1 | 272832n2 | \([0, -1, 0, -1161169, 471769873]\) | \(261883469104/6365529\) | \(4208591759165079552\) | \([2]\) | \(6537216\) | \(2.3579\) |
Rank
sage: E.rank()
The elliptic curves in class 272832n have rank \(1\).
Complex multiplication
The elliptic curves in class 272832n do not have complex multiplication.Modular form 272832.2.a.n
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.