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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 7200bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7200.br2 | 7200bt1 | \([0, 0, 0, 375, 25000]\) | \(64/3\) | \(-273375000000\) | \([2]\) | \(7680\) | \(0.87427\) | \(\Gamma_0(N)\)-optimal |
7200.br1 | 7200bt2 | \([0, 0, 0, -10875, 418750]\) | \(195112/9\) | \(6561000000000\) | \([2]\) | \(15360\) | \(1.2208\) |
Rank
sage: E.rank()
The elliptic curves in class 7200bt have rank \(0\).
Complex multiplication
The elliptic curves in class 7200bt do not have complex multiplication.Modular form 7200.2.a.bt
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 Cremona 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 Cremona labels.