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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 24990.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24990.bv1 | 24990cb2 | \([1, 0, 0, -580546, 170207876]\) | \(63086952699119724103/2809080000\) | \(963514440000\) | \([2]\) | \(245760\) | \(1.7812\) | |
24990.bv2 | 24990cb1 | \([1, 0, 0, -36226, 2666180]\) | \(-15328211694275143/102792499200\) | \(-35257827225600\) | \([2]\) | \(122880\) | \(1.4346\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24990.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 24990.bv do not have complex multiplication.Modular form 24990.2.a.bv
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.