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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 424830w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.w2 | 424830w1 | \([1, 1, 0, -37859728, -116141589248]\) | \(-2113364608155289/828431400960\) | \(-2352547063731806644469760\) | \([2]\) | \(104509440\) | \(3.3856\) | \(\Gamma_0(N)\)-optimal* |
424830.w1 | 424830w2 | \([1, 1, 0, -654146448, -6439366593792]\) | \(10901014250685308569/1040774054400\) | \(2955549418877218021286400\) | \([2]\) | \(209018880\) | \(3.7322\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830w have rank \(0\).
Complex multiplication
The elliptic curves in class 424830w do not have complex multiplication.Modular form 424830.2.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 Cremona 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 Cremona labels.