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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 42432.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42432.bf1 | 42432cb2 | \([0, -1, 0, -3281, -71247]\) | \(238481570896/25857\) | \(423641088\) | \([2]\) | \(32768\) | \(0.68540\) | |
42432.bf2 | 42432cb1 | \([0, -1, 0, -221, -867]\) | \(1171019776/304317\) | \(311620608\) | \([2]\) | \(16384\) | \(0.33883\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42432.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 42432.bf do not have complex multiplication.Modular form 42432.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.