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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 98736.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.ce1 | 98736cu1 | \([0, -1, 0, -379496, -89799312]\) | \(832972004929/610368\) | \(4429021775659008\) | \([2]\) | \(1105920\) | \(1.9365\) | \(\Gamma_0(N)\)-optimal |
| 98736.ce2 | 98736cu2 | \([0, -1, 0, -302056, -127590032]\) | \(-420021471169/727634952\) | \(-5279947584307494912\) | \([2]\) | \(2211840\) | \(2.2830\) |
Rank
sage: E.rank()
The elliptic curves in class 98736.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 98736.ce do not have complex multiplication.Modular form 98736.2.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 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.
