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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 92736fe
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92736.e2 | 92736fe1 | \([0, 0, 0, -12612, -557440]\) | \(-74299881664/1958887\) | \(-5849205239808\) | \([2]\) | \(344064\) | \(1.2324\) | \(\Gamma_0(N)\)-optimal |
92736.e1 | 92736fe2 | \([0, 0, 0, -203052, -35217520]\) | \(38758598383688/25921\) | \(619197530112\) | \([2]\) | \(688128\) | \(1.5789\) |
Rank
sage: E.rank()
The elliptic curves in class 92736fe have rank \(0\).
Complex multiplication
The elliptic curves in class 92736fe do not have complex multiplication.Modular form 92736.2.a.fe
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.