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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 303600.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
303600.bd1 | 303600bd2 | \([0, -1, 0, -201508, 25054012]\) | \(226226123547856/63488926875\) | \(253955707500000000\) | \([2]\) | \(2949120\) | \(2.0467\) | |
303600.bd2 | 303600bd1 | \([0, -1, 0, 32867, 2554012]\) | \(15705460834304/20457421875\) | \(-5114355468750000\) | \([2]\) | \(1474560\) | \(1.7001\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 303600.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 303600.bd do not have complex multiplication.Modular form 303600.2.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.