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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 2898.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2898.l1 | 2898r2 | \([1, -1, 1, -2252381, -1300472859]\) | \(1733490909744055732873/99355964553216\) | \(72430498159294464\) | \([2]\) | \(67584\) | \(2.2988\) | |
2898.l2 | 2898r1 | \([1, -1, 1, -132701, -22729755]\) | \(-354499561600764553/101902222098432\) | \(-74286719909756928\) | \([2]\) | \(33792\) | \(1.9522\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2898.l have rank \(0\).
Complex multiplication
The elliptic curves in class 2898.l do not have complex multiplication.Modular form 2898.2.a.l
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.