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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 66924n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66924.p2 | 66924n1 | \([0, 0, 0, 4056, 54925]\) | \(131072/99\) | \(-5573690117424\) | \([2]\) | \(110592\) | \(1.1339\) | \(\Gamma_0(N)\)-optimal |
66924.p1 | 66924n2 | \([0, 0, 0, -18759, 470158]\) | \(810448/363\) | \(326989820222208\) | \([2]\) | \(221184\) | \(1.4805\) |
Rank
sage: E.rank()
The elliptic curves in class 66924n have rank \(0\).
Complex multiplication
The elliptic curves in class 66924n do not have complex multiplication.Modular form 66924.2.a.n
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.