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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 93600.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.bg1 | 93600f2 | \([0, 0, 0, -78300, 7668000]\) | \(42144192/4225\) | \(5322283200000000\) | \([2]\) | \(442368\) | \(1.7538\) | |
93600.bg2 | 93600f1 | \([0, 0, 0, 6075, 580500]\) | \(1259712/8125\) | \(-159924375000000\) | \([2]\) | \(221184\) | \(1.4073\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 93600.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 93600.bg do not have complex multiplication.Modular form 93600.2.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.