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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 9120.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9120.f1 | 9120e2 | \([0, -1, 0, -2545, -48575]\) | \(445243675456/38475\) | \(157593600\) | \([2]\) | \(6144\) | \(0.61488\) | |
| 9120.f2 | 9120e3 | \([0, -1, 0, -920, 10500]\) | \(168379496648/9774075\) | \(5004326400\) | \([4]\) | \(6144\) | \(0.61488\) | |
| 9120.f3 | 9120e1 | \([0, -1, 0, -170, -600]\) | \(8539701184/2030625\) | \(129960000\) | \([2, 2]\) | \(3072\) | \(0.26831\) | \(\Gamma_0(N)\)-optimal |
| 9120.f4 | 9120e4 | \([0, -1, 0, 400, -4248]\) | \(13789468792/22265625\) | \(-11400000000\) | \([2]\) | \(6144\) | \(0.61488\) |
Rank
sage: E.rank()
The elliptic curves in class 9120.f have rank \(1\).
Complex multiplication
The elliptic curves in class 9120.f do not have complex multiplication.Modular form 9120.2.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.
