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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 405600.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405600.bi1 | 405600bi2 | \([0, -1, 0, -5578408, -5067697688]\) | \(497169541448/190125\) | \(7341576489000000000\) | \([2]\) | \(15482880\) | \(2.5859\) | \(\Gamma_0(N)\)-optimal* |
405600.bi2 | 405600bi1 | \([0, -1, 0, -297158, -103322688]\) | \(-601211584/609375\) | \(-2941336734375000000\) | \([2]\) | \(7741440\) | \(2.2393\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 405600.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 405600.bi do not have complex multiplication.Modular form 405600.2.a.bi
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.