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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 494190.el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
494190.el1 | 494190el2 | \([1, -1, 1, -156548, 23650247]\) | \(651038076963/7220000\) | \(4705377700860000\) | \([2]\) | \(6307840\) | \(1.8216\) | \(\Gamma_0(N)\)-optimal* |
494190.el2 | 494190el1 | \([1, -1, 1, -17828, -320569]\) | \(961504803/486400\) | \(316993866163200\) | \([2]\) | \(3153920\) | \(1.4750\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 494190.el have rank \(0\).
Complex multiplication
The elliptic curves in class 494190.el do not have complex multiplication.Modular form 494190.2.a.el
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.