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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 7350.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7350.bm1 | 7350bd2 | \([1, 0, 1, -143526, 20916718]\) | \(266916252066900625/162\) | \(198450\) | \([]\) | \(25920\) | \(1.2392\) | |
7350.bm2 | 7350bd1 | \([1, 0, 1, -1776, 28438]\) | \(505318200625/4251528\) | \(5208121800\) | \([]\) | \(8640\) | \(0.68990\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7350.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 7350.bm do not have complex multiplication.Modular form 7350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.