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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 439569.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.ba1 | 439569ba2 | \([1, -1, 1, -518261009, -4541072067372]\) | \(36892780289/13\) | \(5424644557202744707821\) | \([2]\) | \(70189056\) | \(3.5252\) | |
439569.ba2 | 439569ba1 | \([1, -1, 1, -32537264, -70276428894]\) | \(9129329/169\) | \(70520379243635681201673\) | \([2]\) | \(35094528\) | \(3.1786\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439569.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.ba do not have complex multiplication.Modular form 439569.2.a.ba
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.