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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 146523.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
146523.n1 | 146523l2 | \([1, 0, 0, -21681, -6833646]\) | \(-276301129/4782969\) | \(-19510922280339009\) | \([]\) | \(739200\) | \(1.8070\) | |
146523.n2 | 146523l1 | \([1, 0, 0, -2896, 60449]\) | \(-658489/9\) | \(-36713242449\) | \([]\) | \(105600\) | \(0.83402\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 146523.n have rank \(0\).
Complex multiplication
The elliptic curves in class 146523.n do not have complex multiplication.Modular form 146523.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.