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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 3600.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3600.bg1 | 3600bm4 | \([0, 0, 0, -119235, 15795650]\) | \(502270291349/1889568\) | \(705277476864000\) | \([2]\) | \(15360\) | \(1.7085\) | |
3600.bg2 | 3600bm2 | \([0, 0, 0, -7635, -256750]\) | \(131872229/18\) | \(6718464000\) | \([2]\) | \(3072\) | \(0.90376\) | |
3600.bg3 | 3600bm3 | \([0, 0, 0, -4035, 474050]\) | \(-19465109/248832\) | \(-92876046336000\) | \([2]\) | \(7680\) | \(1.3619\) | |
3600.bg4 | 3600bm1 | \([0, 0, 0, -435, -4750]\) | \(-24389/12\) | \(-4478976000\) | \([2]\) | \(1536\) | \(0.55718\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3600.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 3600.bg do not have complex multiplication.Modular form 3600.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.