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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1584.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1584.j1 | 1584f1 | \([0, 0, 0, -75, 74]\) | \(62500/33\) | \(24634368\) | \([2]\) | \(256\) | \(0.10986\) | \(\Gamma_0(N)\)-optimal |
| 1584.j2 | 1584f2 | \([0, 0, 0, 285, 578]\) | \(1714750/1089\) | \(-1625868288\) | \([2]\) | \(512\) | \(0.45644\) |
Rank
sage: E.rank()
The elliptic curves in class 1584.j have rank \(1\).
Complex multiplication
The elliptic curves in class 1584.j do not have complex multiplication.Modular form 1584.2.a.j
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.
