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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 70560.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 70560.bz1 | 70560y4 | \([0, 0, 0, -142891203, -657440340298]\) | \(7347751505995469192/72930375\) | \(3202537147814592000\) | \([2]\) | \(5898240\) | \(3.1271\) | |
| 70560.bz2 | 70560y3 | \([0, 0, 0, -12796203, -537544798]\) | \(5276930158229192/3050936350875\) | \(133973491831011177408000\) | \([2]\) | \(5898240\) | \(3.1271\) | |
| 70560.bz3 | 70560y1 | \([0, 0, 0, -8937453, -10256192548]\) | \(14383655824793536/45209390625\) | \(248155780267521000000\) | \([2, 2]\) | \(2949120\) | \(2.7806\) | \(\Gamma_0(N)\)-optimal |
| 70560.bz4 | 70560y2 | \([0, 0, 0, -5186748, -18930823072]\) | \(-43927191786304/415283203125\) | \(-145888171821000000000000\) | \([2]\) | \(5898240\) | \(3.1271\) |
Rank
sage: E.rank()
The elliptic curves in class 70560.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 70560.bz do not have complex multiplication.Modular form 70560.2.a.bz
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.
