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SageMath
sage: E = EllipticCurve("ep1")
sage: E.isogeny_class()
Elliptic curves in class 259920.ep
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.ep1 | 259920ep2 | \([0, 0, 0, -525027, -146426654]\) | \(781484460931/900\) | \(18432777830400\) | \([2]\) | \(1474560\) | \(1.8295\) | |
| 259920.ep2 | 259920ep1 | \([0, 0, 0, -32547, -2327006]\) | \(-186169411/6480\) | \(-132716000378880\) | \([2]\) | \(737280\) | \(1.4829\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.ep have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.ep do not have complex multiplication.Modular form 259920.2.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.
