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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 30960.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.bg1 | 30960ca2 | \([0, 0, 0, -192387, 32479234]\) | \(263732349218689/4160250\) | \(12422439936000\) | \([2]\) | \(110592\) | \(1.6465\) | |
30960.bg2 | 30960ca1 | \([0, 0, 0, -12387, 475234]\) | \(70393838689/8062500\) | \(24074496000000\) | \([2]\) | \(55296\) | \(1.2999\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 30960.bg do not have complex multiplication.Modular form 30960.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.