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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 86490.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86490.bv1 | 86490cd2 | \([1, -1, 1, -4519283, -3697470309]\) | \(-15777367606441/3574920\) | \(-2312938146615499080\) | \([]\) | \(2764800\) | \(2.5159\) | |
86490.bv2 | 86490cd1 | \([1, -1, 1, 21442, -17666769]\) | \(1685159/209250\) | \(-135382695886703250\) | \([]\) | \(921600\) | \(1.9666\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86490.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 86490.bv do not have complex multiplication.Modular form 86490.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.