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SageMath
E = EllipticCurve("nw1")
E.isogeny_class()
Elliptic curves in class 176400.nw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.nw1 | 176400fx1 | \([0, 0, 0, -54075, -1849750]\) | \(1092727/540\) | \(8641624320000000\) | \([2]\) | \(884736\) | \(1.7510\) | \(\Gamma_0(N)\)-optimal |
176400.nw2 | 176400fx2 | \([0, 0, 0, 197925, -14197750]\) | \(53582633/36450\) | \(-583309641600000000\) | \([2]\) | \(1769472\) | \(2.0976\) |
Rank
sage: E.rank()
The elliptic curves in class 176400.nw have rank \(2\).
Complex multiplication
The elliptic curves in class 176400.nw do not have complex multiplication.Modular form 176400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.