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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 139200.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139200.bf1 | 139200cr2 | \([0, -1, 0, -15553, -741023]\) | \(12698260037/7569\) | \(248020992000\) | \([2]\) | \(196608\) | \(1.1306\) | |
| 139200.bf2 | 139200cr1 | \([0, -1, 0, -1153, -6623]\) | \(5177717/2349\) | \(76972032000\) | \([2]\) | \(98304\) | \(0.78400\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139200.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 139200.bf do not have complex multiplication.Modular form 139200.2.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.
