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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 139230eo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139230.a2 | 139230eo1 | \([1, -1, 0, -210, 900]\) | \(38034753147/10519600\) | \(284029200\) | \([2]\) | \(77824\) | \(0.32947\) | \(\Gamma_0(N)\)-optimal |
139230.a1 | 139230eo2 | \([1, -1, 0, -1230, -15624]\) | \(7625597484987/351942500\) | \(9502447500\) | \([2]\) | \(155648\) | \(0.67604\) |
Rank
sage: E.rank()
The elliptic curves in class 139230eo have rank \(2\).
Complex multiplication
The elliptic curves in class 139230eo do not have complex multiplication.Modular form 139230.2.a.eo
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.