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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 66248y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66248.b2 | 66248y1 | \([0, 1, 0, -2760, 3069184]\) | \(-4/7\) | \(-4070486798629888\) | \([2]\) | \(451584\) | \(1.6742\) | \(\Gamma_0(N)\)-optimal |
66248.b1 | 66248y2 | \([0, 1, 0, -334000, 73292064]\) | \(3543122/49\) | \(56986815180818432\) | \([2]\) | \(903168\) | \(2.0208\) |
Rank
sage: E.rank()
The elliptic curves in class 66248y have rank \(1\).
Complex multiplication
The elliptic curves in class 66248y do not have complex multiplication.Modular form 66248.2.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.