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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 60690.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60690.k1 | 60690i2 | \([1, 1, 0, -2554043, 1569831747]\) | \(15537040571177/1786050\) | \(211803876817466850\) | \([2]\) | \(1566720\) | \(2.3515\) | |
60690.k2 | 60690i1 | \([1, 1, 0, -146673, 28633473]\) | \(-2942649737/1296540\) | \(-153753925393420380\) | \([2]\) | \(783360\) | \(2.0050\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 60690.k have rank \(0\).
Complex multiplication
The elliptic curves in class 60690.k do not have complex multiplication.Modular form 60690.2.a.k
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.