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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 443760bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.bv2 | 443760bv1 | \([0, 1, 0, -1110016, 301762484]\) | \(5841725401/1857600\) | \(48097542143272550400\) | \([2]\) | \(12773376\) | \(2.4805\) | \(\Gamma_0(N)\)-optimal |
443760.bv1 | 443760bv2 | \([0, 1, 0, -7026816, -6942767436]\) | \(1481933914201/53916840\) | \(1396031160708485775360\) | \([2]\) | \(25546752\) | \(2.8271\) |
Rank
sage: E.rank()
The elliptic curves in class 443760bv have rank \(0\).
Complex multiplication
The elliptic curves in class 443760bv do not have complex multiplication.Modular form 443760.2.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 Cremona 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 Cremona labels.