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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 406560ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
406560.ce1 | 406560ce1 | \([0, -1, 0, -25450, 1299652]\) | \(16079333824/2953125\) | \(334825029000000\) | \([2]\) | \(1612800\) | \(1.5055\) | \(\Gamma_0(N)\)-optimal |
406560.ce2 | 406560ce2 | \([0, -1, 0, 50175, 7485777]\) | \(1925134784/4465125\) | \(-32400348406272000\) | \([2]\) | \(3225600\) | \(1.8521\) |
Rank
sage: E.rank()
The elliptic curves in class 406560ce have rank \(0\).
Complex multiplication
The elliptic curves in class 406560ce do not have complex multiplication.Modular form 406560.2.a.ce
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.