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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 86394.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86394.bp1 | 86394bq2 | \([1, 1, 1, -46164, -3836403]\) | \(6141556990297/1019592\) | \(1806269423112\) | \([2]\) | \(268800\) | \(1.3598\) | |
86394.bp2 | 86394bq1 | \([1, 1, 1, -2604, -72819]\) | \(-1102302937/616896\) | \(-1092868894656\) | \([2]\) | \(134400\) | \(1.0133\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 86394.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 86394.bp do not have complex multiplication.Modular form 86394.2.a.bp
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.