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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 19350.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19350.bf1 | 19350y2 | \([1, -1, 0, -53442, 4616716]\) | \(1481933914201/53916840\) | \(614146505625000\) | \([2]\) | \(110592\) | \(1.6073\) | |
19350.bf2 | 19350y1 | \([1, -1, 0, -8442, -198284]\) | \(5841725401/1857600\) | \(21159225000000\) | \([2]\) | \(55296\) | \(1.2608\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19350.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 19350.bf do not have complex multiplication.Modular form 19350.2.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.