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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 6720.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6720.bm1 | 6720ce2 | \([0, 1, 0, -5481, -158025]\) | \(4446542056384/25725\) | \(105369600\) | \([2]\) | \(7680\) | \(0.72976\) | |
6720.bm2 | 6720ce1 | \([0, 1, 0, -336, -2646]\) | \(-65743598656/5294205\) | \(-338829120\) | \([2]\) | \(3840\) | \(0.38319\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6720.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 6720.bm do not have complex multiplication.Modular form 6720.2.a.bm
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.