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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 253575.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
253575.bf1 | 253575bf1 | \([1, -1, 1, -1793630, -923806628]\) | \(476196576129/197225\) | \(264300362722265625\) | \([2]\) | \(5308416\) | \(2.3050\) | \(\Gamma_0(N)\)-optimal |
253575.bf2 | 253575bf2 | \([1, -1, 1, -1518005, -1217622878]\) | \(-288673724529/311181605\) | \(-417013112303190703125\) | \([2]\) | \(10616832\) | \(2.6515\) |
Rank
sage: E.rank()
The elliptic curves in class 253575.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 253575.bf do not have complex multiplication.Modular form 253575.2.a.bf
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.