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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 129792.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129792.f1 | 129792b4 | \([0, -1, 0, -437597, -111272955]\) | \(58591911104/243\) | \(38434065186816\) | \([2]\) | \(691200\) | \(1.8161\) | |
| 129792.f2 | 129792b3 | \([0, -1, 0, -26927, -1788333]\) | \(-873722816/59049\) | \(-145929341256192\) | \([2]\) | \(345600\) | \(1.4695\) | |
| 129792.f3 | 129792b2 | \([0, -1, 0, -4957, 131845]\) | \(85184/3\) | \(474494631936\) | \([2]\) | \(138240\) | \(1.0113\) | |
| 129792.f4 | 129792b1 | \([0, -1, 0, 113, 7123]\) | \(64/9\) | \(-22241935872\) | \([2]\) | \(69120\) | \(0.66476\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129792.f have rank \(1\).
Complex multiplication
The elliptic curves in class 129792.f do not have complex multiplication.Modular form 129792.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
