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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 792.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 792.f1 | 792e3 | \([0, 0, 0, -6339, -194258]\) | \(37736227588/33\) | \(24634368\) | \([2]\) | \(768\) | \(0.71863\) | |
| 792.f2 | 792e4 | \([0, 0, 0, -939, 6838]\) | \(122657188/43923\) | \(32788343808\) | \([4]\) | \(768\) | \(0.71863\) | |
| 792.f3 | 792e2 | \([0, 0, 0, -399, -2990]\) | \(37642192/1089\) | \(203233536\) | \([2, 2]\) | \(384\) | \(0.37205\) | |
| 792.f4 | 792e1 | \([0, 0, 0, 6, -155]\) | \(2048/891\) | \(-10392624\) | \([2]\) | \(192\) | \(0.025480\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 792.f have rank \(0\).
Complex multiplication
The elliptic curves in class 792.f do not have complex multiplication.Modular form 792.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
