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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 485520.du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.du1 | 485520du2 | \([0, -1, 0, -2397640, -1051912208]\) | \(15417797707369/4080067320\) | \(403385984864850247680\) | \([2]\) | \(15925248\) | \(2.6624\) | \(\Gamma_0(N)\)-optimal* |
485520.du2 | 485520du1 | \([0, -1, 0, 376760, -106396688]\) | \(59822347031/83966400\) | \(-8301546592999833600\) | \([2]\) | \(7962624\) | \(2.3159\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.du have rank \(0\).
Complex multiplication
The elliptic curves in class 485520.du do not have complex multiplication.Modular form 485520.2.a.du
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.