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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 129472.dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129472.dl1 | 129472j2 | \([0, -1, 0, -2377121, -267159007]\) | \(234770924809/130960928\) | \(828657745501626564608\) | \([2]\) | \(8847360\) | \(2.7042\) | |
129472.dl2 | 129472j1 | \([0, -1, 0, 582239, -33369567]\) | \(3449795831/2071552\) | \(-13107784407341596672\) | \([2]\) | \(4423680\) | \(2.3576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129472.dl have rank \(1\).
Complex multiplication
The elliptic curves in class 129472.dl do not have complex multiplication.Modular form 129472.2.a.dl
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.