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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 108900bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
108900.bi2 | 108900bt1 | \([0, 0, 0, 825, -63250]\) | \(176/5\) | \(-1764180000000\) | \([]\) | \(103680\) | \(1.0300\) | \(\Gamma_0(N)\)-optimal |
108900.bi1 | 108900bt2 | \([0, 0, 0, -98175, -11844250]\) | \(-296587984/125\) | \(-44104500000000\) | \([]\) | \(311040\) | \(1.5793\) |
Rank
sage: E.rank()
The elliptic curves in class 108900bt have rank \(0\).
Complex multiplication
The elliptic curves in class 108900bt do not have complex multiplication.Modular form 108900.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.