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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 468270p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
468270.p2 | 468270p1 | \([1, -1, 0, 4680, -214164]\) | \(11681631109/26958420\) | \(-26157727967580\) | \([2]\) | \(1751040\) | \(1.2586\) | \(\Gamma_0(N)\)-optimal* |
468270.p1 | 468270p2 | \([1, -1, 0, -37890, -2334150]\) | \(6200095678811/1142598150\) | \(1108661842346850\) | \([2]\) | \(3502080\) | \(1.6052\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 468270p have rank \(0\).
Complex multiplication
The elliptic curves in class 468270p do not have complex multiplication.Modular form 468270.2.a.p
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.