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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 8470.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8470.y1 | 8470w2 | \([1, -1, 1, -99243, -12008719]\) | \(45844273539/350\) | \(825281691850\) | \([2]\) | \(42240\) | \(1.4612\) | |
8470.y2 | 8470w1 | \([1, -1, 1, -6073, -194763]\) | \(-10503459/980\) | \(-2310788737180\) | \([2]\) | \(21120\) | \(1.1146\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8470.y have rank \(1\).
Complex multiplication
The elliptic curves in class 8470.y do not have complex multiplication.Modular form 8470.2.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 LMFDB 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 LMFDB labels.