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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 257600dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.dl1 | 257600dl1 | \([0, 0, 0, -260300, -51098000]\) | \(476196576129/197225\) | \(807833600000000\) | \([2]\) | \(1769472\) | \(1.8224\) | \(\Gamma_0(N)\)-optimal |
257600.dl2 | 257600dl2 | \([0, 0, 0, -220300, -67338000]\) | \(-288673724529/311181605\) | \(-1274599854080000000\) | \([2]\) | \(3538944\) | \(2.1690\) |
Rank
sage: E.rank()
The elliptic curves in class 257600dl have rank \(0\).
Complex multiplication
The elliptic curves in class 257600dl do not have complex multiplication.Modular form 257600.2.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.