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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 259182.du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.du1 | 259182du1 | \([1, -1, 1, -12117326, -14878760839]\) | \(152356299470130673/14087536440516\) | \(18193602075046687832004\) | \([2]\) | \(24330240\) | \(3.0101\) | \(\Gamma_0(N)\)-optimal |
| 259182.du2 | 259182du2 | \([1, -1, 1, 14029564, -70352002663]\) | \(236468134693587887/1792270835082882\) | \(-2314660375282423563206658\) | \([2]\) | \(48660480\) | \(3.3566\) |
Rank
sage: E.rank()
The elliptic curves in class 259182.du have rank \(0\).
Complex multiplication
The elliptic curves in class 259182.du do not have complex multiplication.Modular form 259182.2.a.du
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.
