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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 333795.bp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333795.bp1 | 333795bp2 | \([1, 1, 0, -468001837, 3262340405854]\) | \(95593000698598946633/16544834717362875\) | \(1962016816125906522032848875\) | \([2]\) | \(175472640\) | \(3.9571\) | |
333795.bp2 | 333795bp1 | \([1, 1, 0, -446507462, 3631231168479]\) | \(83017487374717676633/3329226140625\) | \(394805858395021454390625\) | \([2]\) | \(87736320\) | \(3.6106\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333795.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 333795.bp do not have complex multiplication.Modular form 333795.2.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.