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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 7350.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.bg1 | 7350bl4 | \([1, 0, 1, -1014326, -392004952]\) | \(502270291349/1889568\) | \(434190987562500000\) | \([2]\) | \(144000\) | \(2.2437\) | |
7350.bg2 | 7350bl2 | \([1, 0, 1, -64951, 6365048]\) | \(131872229/18\) | \(4136097656250\) | \([2]\) | \(28800\) | \(1.4390\) | |
7350.bg3 | 7350bl3 | \([1, 0, 1, -34326, -11764952]\) | \(-19465109/248832\) | \(-57177414000000000\) | \([2]\) | \(72000\) | \(1.8971\) | |
7350.bg4 | 7350bl1 | \([1, 0, 1, -3701, 117548]\) | \(-24389/12\) | \(-2757398437500\) | \([2]\) | \(14400\) | \(1.0924\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7350.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 7350.bg do not have complex multiplication.Modular form 7350.2.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.