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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 80688.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80688.bf1 | 80688w2 | \([0, 1, 0, -4988, 133944]\) | \(31899394000/3\) | \(1291008\) | \([]\) | \(48384\) | \(0.60794\) | |
80688.bf2 | 80688w1 | \([0, 1, 0, -68, 120]\) | \(82000/27\) | \(11619072\) | \([]\) | \(16128\) | \(0.058630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 80688.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 80688.bf do not have complex multiplication.Modular form 80688.2.a.bf
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.