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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 344760.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
344760.bd1 | 344760bd1 | \([0, -1, 0, -60220, -5645420]\) | \(19545784144/89505\) | \(110598026123520\) | \([2]\) | \(1204224\) | \(1.5456\) | \(\Gamma_0(N)\)-optimal |
344760.bd2 | 344760bd2 | \([0, -1, 0, -29800, -11376548]\) | \(-592143556/10989225\) | \(-54315919496217600\) | \([2]\) | \(2408448\) | \(1.8922\) |
Rank
sage: E.rank()
The elliptic curves in class 344760.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 344760.bd do not have complex multiplication.Modular form 344760.2.a.bd
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.