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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 154560.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.f1 | 154560hv6 | \([0, -1, 0, -5420161, -4855168895]\) | \(67176973097223766561/91487391870\) | \(23982870854369280\) | \([2]\) | \(3145728\) | \(2.4172\) | |
| 154560.f2 | 154560hv4 | \([0, -1, 0, -341761, -74363135]\) | \(16840406336564161/604708416900\) | \(158520683239833600\) | \([2, 2]\) | \(1572864\) | \(2.0706\) | |
| 154560.f3 | 154560hv2 | \([0, -1, 0, -53761, 3224065]\) | \(65553197996161/20996010000\) | \(5503978045440000\) | \([2, 2]\) | \(786432\) | \(1.7240\) | |
| 154560.f4 | 154560hv1 | \([0, -1, 0, -48641, 4144641]\) | \(48551226272641/9273600\) | \(2431018598400\) | \([2]\) | \(393216\) | \(1.3774\) | \(\Gamma_0(N)\)-optimal |
| 154560.f5 | 154560hv5 | \([0, -1, 0, 128639, -263746175]\) | \(898045580910239/115117148363070\) | \(-30177269740488622080\) | \([2]\) | \(3145728\) | \(2.4172\) | |
| 154560.f6 | 154560hv3 | \([0, -1, 0, 152319, 21812481]\) | \(1490881681033919/1650501562500\) | \(-432669081600000000\) | \([2]\) | \(1572864\) | \(2.0706\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.f have rank \(1\).
Complex multiplication
The elliptic curves in class 154560.f do not have complex multiplication.Modular form 154560.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
