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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 4950.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4950.bm1 | 4950bj1 | \([1, -1, 1, -230, -3603]\) | \(-117649/440\) | \(-5011875000\) | \([]\) | \(2880\) | \(0.54692\) | \(\Gamma_0(N)\)-optimal |
4950.bm2 | 4950bj2 | \([1, -1, 1, 2020, 86397]\) | \(80062991/332750\) | \(-3790230468750\) | \([]\) | \(8640\) | \(1.0962\) |
Rank
sage: E.rank()
The elliptic curves in class 4950.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 4950.bm do not have complex multiplication.Modular form 4950.2.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.