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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 54096.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54096.bf1 | 54096bl1 | \([0, -1, 0, -255432, 49774320]\) | \(1311889499494111/438012\) | \(615375323136\) | \([2]\) | \(184320\) | \(1.6201\) | \(\Gamma_0(N)\)-optimal |
54096.bf2 | 54096bl2 | \([0, -1, 0, -254312, 50231280]\) | \(-1294708239486271/23981814018\) | \(-33692722004680704\) | \([2]\) | \(368640\) | \(1.9667\) |
Rank
sage: E.rank()
The elliptic curves in class 54096.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 54096.bf do not have complex multiplication.Modular form 54096.2.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.