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SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 485100dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 485100.dj1 | 485100dj1 | \([0, 0, 0, -42100800, -105143777375]\) | \(10392086293512192/1684375\) | \(1337613982031250000\) | \([2]\) | \(28753920\) | \(2.8800\) | \(\Gamma_0(N)\)-optimal |
| 485100.dj2 | 485100dj2 | \([0, 0, 0, -41972175, -105818158250]\) | \(-643570518871152/8271484375\) | \(-105098241445312500000000\) | \([2]\) | \(57507840\) | \(3.2266\) |
Rank
sage: E.rank()
The elliptic curves in class 485100dj have rank \(1\).
Complex multiplication
The elliptic curves in class 485100dj do not have complex multiplication.Modular form 485100.2.a.dj
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.
