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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 44100bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.v2 | 44100bx1 | \([0, 0, 0, -342300, 66450125]\) | \(70954958848/10546875\) | \(659303613281250000\) | \([2]\) | \(442368\) | \(2.1437\) | \(\Gamma_0(N)\)-optimal |
44100.v1 | 44100bx2 | \([0, 0, 0, -5264175, 4648715750]\) | \(16129950234928/455625\) | \(455710657500000000\) | \([2]\) | \(884736\) | \(2.4902\) |
Rank
sage: E.rank()
The elliptic curves in class 44100bx have rank \(0\).
Complex multiplication
The elliptic curves in class 44100bx do not have complex multiplication.Modular form 44100.2.a.bx
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 Cremona 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 Cremona labels.