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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 277350.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.w1 | 277350w1 | \([1, 1, 0, -88591175, -320434996875]\) | \(778510269523657/1540767744\) | \(152183629437698304000000\) | \([2]\) | \(46362624\) | \(3.3361\) | \(\Gamma_0(N)\)-optimal |
277350.w2 | 277350w2 | \([1, 1, 0, -59007175, -537847812875]\) | \(-230042158153417/1131994839168\) | \(-111808599187113954738000000\) | \([2]\) | \(92725248\) | \(3.6827\) |
Rank
sage: E.rank()
The elliptic curves in class 277350.w have rank \(2\).
Complex multiplication
The elliptic curves in class 277350.w do not have complex multiplication.Modular form 277350.2.a.w
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.