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SageMath
E = EllipticCurve("es1")
E.isogeny_class()
Elliptic curves in class 92736es
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.s2 | 92736es1 | \([0, 0, 0, -2316, 39440]\) | \(7189057/644\) | \(123070316544\) | \([2]\) | \(110592\) | \(0.86776\) | \(\Gamma_0(N)\)-optimal |
92736.s1 | 92736es2 | \([0, 0, 0, -8076, -234736]\) | \(304821217/51842\) | \(9907160481792\) | \([2]\) | \(221184\) | \(1.2143\) |
Rank
sage: E.rank()
The elliptic curves in class 92736es have rank \(0\).
Complex multiplication
The elliptic curves in class 92736es do not have complex multiplication.Modular form 92736.2.a.es
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.