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SageMath
E = EllipticCurve("nw1")
E.isogeny_class()
Elliptic curves in class 235200.nw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.nw1 | 235200nw2 | \([0, -1, 0, -229640833, -1339358890463]\) | \(266916252066900625/162\) | \(812851200000000\) | \([]\) | \(24883200\) | \(3.0836\) | |
235200.nw2 | 235200nw1 | \([0, -1, 0, -2840833, -1828570463]\) | \(505318200625/4251528\) | \(21332466892800000000\) | \([]\) | \(8294400\) | \(2.5343\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235200.nw have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.nw do not have complex multiplication.Modular form 235200.2.a.nw
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.