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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1584c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1584.n4 | 1584c1 | \([0, 0, 0, 6, 155]\) | \(2048/891\) | \(-10392624\) | \([2]\) | \(384\) | \(0.025480\) | \(\Gamma_0(N)\)-optimal |
| 1584.n3 | 1584c2 | \([0, 0, 0, -399, 2990]\) | \(37642192/1089\) | \(203233536\) | \([2, 2]\) | \(768\) | \(0.37205\) | |
| 1584.n2 | 1584c3 | \([0, 0, 0, -939, -6838]\) | \(122657188/43923\) | \(32788343808\) | \([2]\) | \(1536\) | \(0.71863\) | |
| 1584.n1 | 1584c4 | \([0, 0, 0, -6339, 194258]\) | \(37736227588/33\) | \(24634368\) | \([4]\) | \(1536\) | \(0.71863\) |
Rank
sage: E.rank()
The elliptic curves in class 1584c have rank \(0\).
Complex multiplication
The elliptic curves in class 1584c do not have complex multiplication.Modular form 1584.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
