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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 440818.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440818.d1 | 440818d2 | \([1, 0, 1, -238235, 44681478]\) | \(582810602977/829472\) | \(2128198215926048\) | \([2]\) | \(4158720\) | \(1.8441\) | \(\Gamma_0(N)\)-optimal* |
440818.d2 | 440818d1 | \([1, 0, 1, -19195, 260166]\) | \(304821217/164864\) | \(422995918693376\) | \([2]\) | \(2079360\) | \(1.4975\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 440818.d have rank \(1\).
Complex multiplication
The elliptic curves in class 440818.d do not have complex multiplication.Modular form 440818.2.a.d
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.