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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 10816.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10816.bm1 | 10816p2 | \([0, 0, 0, -2300428, -1473466384]\) | \(-1064019559329/125497034\) | \(-158793783885039140864\) | \([]\) | \(451584\) | \(2.6120\) | |
10816.bm2 | 10816p1 | \([0, 0, 0, -29068, 2917616]\) | \(-2146689/1664\) | \(-2105490846777344\) | \([]\) | \(64512\) | \(1.6390\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10816.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 10816.bm do not have complex multiplication.Modular form 10816.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.