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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 450800.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450800.bv1 | 450800bv2 | \([0, 1, 0, -3097208, -4838650412]\) | \(-17455277065/43606528\) | \(-8208423060275200000000\) | \([]\) | \(29859840\) | \(2.8928\) | |
450800.bv2 | 450800bv1 | \([0, 1, 0, 332792, 148569588]\) | \(21653735/63112\) | \(-11880101900800000000\) | \([]\) | \(9953280\) | \(2.3435\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 450800.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 450800.bv do not have complex multiplication.Modular form 450800.2.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.