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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 490960.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
490960.bm1 | 490960bm1 | \([0, 0, 0, -10108, 390963]\) | \(151732224/85\) | \(63982398160\) | \([2]\) | \(691200\) | \(1.0207\) | \(\Gamma_0(N)\)-optimal |
490960.bm2 | 490960bm2 | \([0, 0, 0, -8303, 535002]\) | \(-5256144/7225\) | \(-87016061497600\) | \([2]\) | \(1382400\) | \(1.3672\) |
Rank
sage: E.rank()
The elliptic curves in class 490960.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 490960.bm do not have complex multiplication.Modular form 490960.2.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.