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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 89280.dx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89280.dx1 | 89280fh2 | \([0, 0, 0, -21566892, 35962375376]\) | \(5805223604235668521/435937500000000\) | \(83308953600000000000000\) | \([2]\) | \(8257536\) | \(3.1434\) | |
| 89280.dx2 | 89280fh1 | \([0, 0, 0, 1288788, 2492517584]\) | \(1238798620042199/14760960000000\) | \(-2820863384616960000000\) | \([2]\) | \(4128768\) | \(2.7968\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 89280.dx have rank \(0\).
Complex multiplication
The elliptic curves in class 89280.dx do not have complex multiplication.Modular form 89280.2.a.dx
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.
