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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 228150bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
228150.hg2 | 228150bu1 | \([1, -1, 1, 30895, -27719103]\) | \(1601613/163840\) | \(-333629038080000000\) | \([]\) | \(2954880\) | \(2.0418\) | \(\Gamma_0(N)\)-optimal |
228150.hg1 | 228150bu2 | \([1, -1, 1, -6053105, -5731807103]\) | \(-16522921323/4000\) | \(-5937880096687500000\) | \([]\) | \(8864640\) | \(2.5911\) |
Rank
sage: E.rank()
The elliptic curves in class 228150bu have rank \(1\).
Complex multiplication
The elliptic curves in class 228150bu do not have complex multiplication.Modular form 228150.2.a.bu
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.