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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 102960.bv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.bv1 | 102960w2 | \([0, 0, 0, -10443, -410582]\) | \(168722134564/83655\) | \(62448122880\) | \([2]\) | \(131072\) | \(1.0246\) | |
| 102960.bv2 | 102960w1 | \([0, 0, 0, -543, -8642]\) | \(-94875856/117975\) | \(-22016966400\) | \([2]\) | \(65536\) | \(0.67803\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.bv have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.bv do not have complex multiplication.Modular form 102960.2.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.
