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SageMath
E = EllipticCurve("ep1")
E.isogeny_class()
Elliptic curves in class 123840.ep
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123840.ep1 | 123840gj1 | \([0, 0, 0, -11532, -383344]\) | \(3550014724/725625\) | \(34667274240000\) | \([2]\) | \(294912\) | \(1.3136\) | \(\Gamma_0(N)\)-optimal |
123840.ep2 | 123840gj2 | \([0, 0, 0, 24468, -2298544]\) | \(16954370638/33698025\) | \(-3219896431411200\) | \([2]\) | \(589824\) | \(1.6602\) |
Rank
sage: E.rank()
The elliptic curves in class 123840.ep have rank \(1\).
Complex multiplication
The elliptic curves in class 123840.ep do not have complex multiplication.Modular form 123840.2.a.ep
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.