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SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 97020.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97020.bv1 | 97020r1 | \([0, 0, 0, -672, 4361]\) | \(226492416/75625\) | \(11205810000\) | \([2]\) | \(61440\) | \(0.63091\) | \(\Gamma_0(N)\)-optimal |
97020.bv2 | 97020r2 | \([0, 0, 0, 1953, 30086]\) | \(347482224/366025\) | \(-867777926400\) | \([2]\) | \(122880\) | \(0.97748\) |
Rank
sage: E.rank()
The elliptic curves in class 97020.bv have rank \(2\).
Complex multiplication
The elliptic curves in class 97020.bv do not have complex multiplication.Modular form 97020.2.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.