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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 308550.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.bz1 | 308550bz4 | \([1, 1, 0, -666599650, 6573377207500]\) | \(1183430669265454849849/10449720703125000\) | \(289254963414825439453125000\) | \([2]\) | \(199065600\) | \(3.9009\) | |
308550.bz2 | 308550bz3 | \([1, 1, 0, -72126650, -67480675500]\) | \(1499114720492202169/796539777000000\) | \(22048731310654640625000000\) | \([2]\) | \(99532800\) | \(3.5544\) | |
308550.bz3 | 308550bz2 | \([1, 1, 0, -57168025, -161023431125]\) | \(746461053445307689/27443694341250\) | \(759659040482487363281250\) | \([2]\) | \(66355200\) | \(3.3516\) | |
308550.bz4 | 308550bz1 | \([1, 1, 0, -56653775, -164154699375]\) | \(726497538898787209/1038579300\) | \(28748540363864062500\) | \([2]\) | \(33177600\) | \(3.0050\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 308550.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 308550.bz do not have complex multiplication.Modular form 308550.2.a.bz
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.