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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1584.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1584.f1 | 1584n3 | \([0, 0, 0, -50691, -4392830]\) | \(4824238966273/66\) | \(197074944\) | \([2]\) | \(3072\) | \(1.1475\) | |
| 1584.f2 | 1584n2 | \([0, 0, 0, -3171, -68510]\) | \(1180932193/4356\) | \(13006946304\) | \([2, 2]\) | \(1536\) | \(0.80093\) | |
| 1584.f3 | 1584n4 | \([0, 0, 0, -1731, -131006]\) | \(-192100033/2371842\) | \(-7082282262528\) | \([2]\) | \(3072\) | \(1.1475\) | |
| 1584.f4 | 1584n1 | \([0, 0, 0, -291, 34]\) | \(912673/528\) | \(1576599552\) | \([2]\) | \(768\) | \(0.45435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1584.f have rank \(1\).
Complex multiplication
The elliptic curves in class 1584.f do not have complex multiplication.Modular form 1584.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
