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SageMath
E = EllipticCurve("iw1")
E.isogeny_class()
Elliptic curves in class 428400iw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
428400.iw2 | 428400iw1 | \([0, 0, 0, 113325, -2848750]\) | \(3449795831/2071552\) | \(-96650330112000000\) | \([2]\) | \(3686400\) | \(1.9484\) | \(\Gamma_0(N)\)-optimal* |
428400.iw1 | 428400iw2 | \([0, 0, 0, -462675, -23008750]\) | \(234770924809/130960928\) | \(6110113056768000000\) | \([2]\) | \(7372800\) | \(2.2950\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 428400iw have rank \(0\).
Complex multiplication
The elliptic curves in class 428400iw do not have complex multiplication.Modular form 428400.2.a.iw
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.