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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 11400.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11400.bg1 | 11400bj4 | \([0, 1, 0, -760008, 254767488]\) | \(3034301922374404/1425\) | \(22800000000\) | \([2]\) | \(49152\) | \(1.7612\) | |
| 11400.bg2 | 11400bj3 | \([0, 1, 0, -57008, 2257488]\) | \(1280615525284/601171875\) | \(9618750000000000\) | \([2]\) | \(49152\) | \(1.7612\) | |
| 11400.bg3 | 11400bj2 | \([0, 1, 0, -47508, 3967488]\) | \(2964647793616/2030625\) | \(8122500000000\) | \([2, 2]\) | \(24576\) | \(1.4146\) | |
| 11400.bg4 | 11400bj1 | \([0, 1, 0, -2383, 86738]\) | \(-5988775936/9774075\) | \(-2443518750000\) | \([2]\) | \(12288\) | \(1.0680\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11400.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 11400.bg do not have complex multiplication.Modular form 11400.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
