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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 296450bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
296450.bu2 | 296450bu1 | \([1, 1, 0, 663925, 174977125]\) | \(397535/392\) | \(-31914676951128125000\) | \([]\) | \(7776000\) | \(2.4295\) | \(\Gamma_0(N)\)-optimal |
296450.bu1 | 296450bu2 | \([1, 1, 0, -6747325, -9481881625]\) | \(-417267265/235298\) | \(-19156784839914657031250\) | \([]\) | \(23328000\) | \(2.9788\) |
Rank
sage: E.rank()
The elliptic curves in class 296450bu have rank \(0\).
Complex multiplication
The elliptic curves in class 296450bu do not have complex multiplication.Modular form 296450.2.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.