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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 7744.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7744.be1 | 7744bc2 | \([0, -1, 0, -19521, -4097311]\) | \(-121\) | \(-6799340234604544\) | \([]\) | \(33792\) | \(1.7207\) | |
7744.be2 | 7744bc1 | \([0, -1, 0, -1921, 33057]\) | \(-24729001\) | \(-31719424\) | \([]\) | \(3072\) | \(0.52176\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7744.be have rank \(1\).
Complex multiplication
The elliptic curves in class 7744.be do not have complex multiplication.Modular form 7744.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.