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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 159120dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.ee1 | 159120dl1 | \([0, 0, 0, -3207, -69626]\) | \(19545784144/89505\) | \(16703781120\) | \([2]\) | \(114688\) | \(0.81244\) | \(\Gamma_0(N)\)-optimal |
159120.ee2 | 159120dl2 | \([0, 0, 0, -1587, -139934]\) | \(-592143556/10989225\) | \(-8203412505600\) | \([2]\) | \(229376\) | \(1.1590\) |
Rank
sage: E.rank()
The elliptic curves in class 159120dl have rank \(1\).
Complex multiplication
The elliptic curves in class 159120dl do not have complex multiplication.Modular form 159120.2.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 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.