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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 69828y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69828.v2 | 69828y1 | \([0, 1, 0, 1411, 11736]\) | \(131072/99\) | \(-234488848176\) | \([2]\) | \(76032\) | \(0.86988\) | \(\Gamma_0(N)\)-optimal |
69828.v1 | 69828y2 | \([0, 1, 0, -6524, 94260]\) | \(810448/363\) | \(13756679092992\) | \([2]\) | \(152064\) | \(1.2165\) |
Rank
sage: E.rank()
The elliptic curves in class 69828y have rank \(0\).
Complex multiplication
The elliptic curves in class 69828y do not have complex multiplication.Modular form 69828.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.