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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 270725.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270725.bz1 | 270725bz2 | \([1, -1, 0, -14354167, -20928622884]\) | \(177930109857804849/634933\) | \(1167175508078125\) | \([2]\) | \(6912000\) | \(2.5328\) | |
270725.bz2 | 270725bz1 | \([1, -1, 0, -897542, -326530009]\) | \(43499078731809/82055753\) | \(150840270073390625\) | \([2]\) | \(3456000\) | \(2.1863\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270725.bz have rank \(1\).
Complex multiplication
The elliptic curves in class 270725.bz do not have complex multiplication.Modular form 270725.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.