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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 4560.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4560.r1 | 4560z2 | \([0, 1, 0, -25896, -1612620]\) | \(468898230633769/5540400\) | \(22693478400\) | \([2]\) | \(9216\) | \(1.1371\) | |
4560.r2 | 4560z1 | \([0, 1, 0, -1576, -26956]\) | \(-105756712489/12476160\) | \(-51102351360\) | \([2]\) | \(4608\) | \(0.79056\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.r have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.r do not have complex multiplication.Modular form 4560.2.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 LMFDB 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 LMFDB labels.