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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 5550bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.bc2 | 5550bd1 | \([1, 1, 1, -48, 81]\) | \(97972181/21312\) | \(2664000\) | \([2]\) | \(1536\) | \(-0.053240\) | \(\Gamma_0(N)\)-optimal |
5550.bc1 | 5550bd2 | \([1, 1, 1, -248, -1519]\) | \(13498272341/887112\) | \(110889000\) | \([2]\) | \(3072\) | \(0.29333\) |
Rank
sage: E.rank()
The elliptic curves in class 5550bd have rank \(1\).
Complex multiplication
The elliptic curves in class 5550bd do not have complex multiplication.Modular form 5550.2.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 Cremona 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 Cremona labels.