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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 409101y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.y1 | 409101y1 | \([0, -1, 1, -36703, 2719254]\) | \(-62992384000/14283\) | \(-1239857082387\) | \([]\) | \(829440\) | \(1.3126\) | \(\Gamma_0(N)\)-optimal |
409101.y2 | 409101y2 | \([0, -1, 1, 14117, 9419871]\) | \(3584000000/444107667\) | \(-38551427310251163\) | \([]\) | \(2488320\) | \(1.8619\) |
Rank
sage: E.rank()
The elliptic curves in class 409101y have rank \(1\).
Complex multiplication
The elliptic curves in class 409101y do not have complex multiplication.Modular form 409101.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.