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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 328560.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 328560.n1 | 328560n2 | \([0, -1, 0, -1232556, 365108700]\) | \(6224272/1875\) | \(62381635101636960000\) | \([2]\) | \(8695296\) | \(2.5035\) | |
| 328560.n2 | 328560n1 | \([0, -1, 0, -472761, -120552264]\) | \(5619712/225\) | \(467862263262277200\) | \([2]\) | \(4347648\) | \(2.1570\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 328560.n have rank \(1\).
Complex multiplication
The elliptic curves in class 328560.n do not have complex multiplication.Modular form 328560.2.a.n
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.
