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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 15600.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.bf1 | 15600f3 | \([0, -1, 0, -208008, -36445488]\) | \(31103978031362/195\) | \(6240000000\) | \([2]\) | \(73728\) | \(1.4851\) | |
| 15600.bf2 | 15600f4 | \([0, -1, 0, -18008, -85488]\) | \(20183398562/11567205\) | \(370150560000000\) | \([2]\) | \(73728\) | \(1.4851\) | |
| 15600.bf3 | 15600f2 | \([0, -1, 0, -13008, -565488]\) | \(15214885924/38025\) | \(608400000000\) | \([2, 2]\) | \(36864\) | \(1.1385\) | |
| 15600.bf4 | 15600f1 | \([0, -1, 0, -508, -15488]\) | \(-3631696/24375\) | \(-97500000000\) | \([2]\) | \(18432\) | \(0.79195\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 15600.bf do not have complex multiplication.Modular form 15600.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
