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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 4928.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4928.e1 | 4928r2 | \([0, 1, 0, -91169, 7401151]\) | \(1278763167594532/375974556419\) | \(24639868529475584\) | \([2]\) | \(30720\) | \(1.8511\) | |
4928.e2 | 4928r1 | \([0, 1, 0, 15311, 778095]\) | \(24226243449392/29774625727\) | \(-487827467911168\) | \([2]\) | \(15360\) | \(1.5045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4928.e have rank \(1\).
Complex multiplication
The elliptic curves in class 4928.e do not have complex multiplication.Modular form 4928.2.a.e
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.