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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4928.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4928.f1 | 4928z2 | \([0, 1, 0, -5153, 140671]\) | \(461889917000/5929\) | \(194281472\) | \([2]\) | \(3072\) | \(0.73580\) | |
4928.f2 | 4928z1 | \([0, 1, 0, -313, 2247]\) | \(-830584000/102487\) | \(-419786752\) | \([2]\) | \(1536\) | \(0.38922\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4928.f have rank \(1\).
Complex multiplication
The elliptic curves in class 4928.f do not have complex multiplication.Modular form 4928.2.a.f
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.