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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 74970.cd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
74970.cd1 | 74970co2 | \([1, -1, 1, -16618433, -26038940623]\) | \(5918043195362419129/8515734343200\) | \(730361502082746727200\) | \([2]\) | \(5898240\) | \(2.9058\) | |
74970.cd2 | 74970co1 | \([1, -1, 1, -742433, -643691023]\) | \(-527690404915129/1782829440000\) | \(-152906365473402240000\) | \([2]\) | \(2949120\) | \(2.5592\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 74970.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 74970.cd do not have complex multiplication.Modular form 74970.2.a.cd
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.