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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 489762o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489762.o2 | 489762o1 | \([1, -1, 0, 40782, 70477460]\) | \(35937/10304\) | \(-2150737033379852736\) | \([2]\) | \(8266752\) | \(2.1969\) | \(\Gamma_0(N)\)-optimal* |
489762.o1 | 489762o2 | \([1, -1, 0, -2331978, 1334209436]\) | \(6719171103/207368\) | \(43283582796769536312\) | \([2]\) | \(16533504\) | \(2.5434\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 489762o have rank \(1\).
Complex multiplication
The elliptic curves in class 489762o do not have complex multiplication.Modular form 489762.2.a.o
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.