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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 65520r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65520.k1 | 65520r1 | \([0, 0, 0, -2523, -45862]\) | \(2379293284/159705\) | \(119219143680\) | \([2]\) | \(61440\) | \(0.87433\) | \(\Gamma_0(N)\)-optimal |
65520.k2 | 65520r2 | \([0, 0, 0, 2157, -196558]\) | \(743389918/11609325\) | \(-17332629350400\) | \([2]\) | \(122880\) | \(1.2209\) |
Rank
sage: E.rank()
The elliptic curves in class 65520r have rank \(1\).
Complex multiplication
The elliptic curves in class 65520r do not have complex multiplication.Modular form 65520.2.a.r
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.