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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 60690be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60690.be2 | 60690be1 | \([1, 0, 1, -486538, -341619844]\) | \(-527690404915129/1782829440000\) | \(-43033168623231360000\) | \([2]\) | \(2211840\) | \(2.4535\) | \(\Gamma_0(N)\)-optimal |
60690.be1 | 60690be2 | \([1, 0, 1, -10890538, -13816880644]\) | \(5918043195362419129/8515734343200\) | \(205549125294659680800\) | \([2]\) | \(4423680\) | \(2.8001\) |
Rank
sage: E.rank()
The elliptic curves in class 60690be have rank \(0\).
Complex multiplication
The elliptic curves in class 60690be do not have complex multiplication.Modular form 60690.2.a.be
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.