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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 13200.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13200.bu1 | 13200ce2 | \([0, 1, 0, -308, 888]\) | \(810448/363\) | \(1452000000\) | \([2]\) | \(6144\) | \(0.45343\) | |
13200.bu2 | 13200ce1 | \([0, 1, 0, 67, 138]\) | \(131072/99\) | \(-24750000\) | \([2]\) | \(3072\) | \(0.10685\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13200.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 13200.bu do not have complex multiplication.Modular form 13200.2.a.bu
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.