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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 66924.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66924.n1 | 66924j2 | \([0, 0, 0, -1965639, -1060698418]\) | \(932410994128/29403\) | \(26486175437998848\) | \([2]\) | \(921600\) | \(2.2471\) | |
66924.n2 | 66924j1 | \([0, 0, 0, -117624, -18048355]\) | \(-3196715008/649539\) | \(-36568980860418864\) | \([2]\) | \(460800\) | \(1.9006\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66924.n have rank \(1\).
Complex multiplication
The elliptic curves in class 66924.n 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 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.