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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 92736.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.z1 | 92736bg2 | \([0, 0, 0, -100236, -12199696]\) | \(582810602977/829472\) | \(158514567708672\) | \([2]\) | \(368640\) | \(1.6277\) | |
92736.z2 | 92736bg1 | \([0, 0, 0, -8076, -71440]\) | \(304821217/164864\) | \(31506001035264\) | \([2]\) | \(184320\) | \(1.2811\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92736.z have rank \(0\).
Complex multiplication
The elliptic curves in class 92736.z do not have complex multiplication.Modular form 92736.2.a.z
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.