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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 338910cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338910.cn4 | 338910cn1 | \([1, 0, 0, -2469093165, 62319962497617]\) | \(-1664700629958202478932584096762961/714434636321013104640000000000\) | \(-714434636321013104640000000000\) | \([10]\) | \(541440000\) | \(4.4360\) | \(\Gamma_0(N)\)-optimal |
338910.cn2 | 338910cn2 | \([1, 0, 0, -42917093165, 3421777140097617]\) | \(8742076626521910595251756451488762961/964148342166520646557593600000\) | \(964148342166520646557593600000\) | \([10]\) | \(1082880000\) | \(4.7826\) | |
338910.cn3 | 338910cn3 | \([1, 0, 0, -19953261165, -6053922020220783]\) | \(-878547754640224469469830258471034961/15324360292462134906363408448382400\) | \(-15324360292462134906363408448382400\) | \([2]\) | \(2707200000\) | \(5.2407\) | |
338910.cn1 | 338910cn4 | \([1, 0, 0, -635364540965, -194182565527705623]\) | \(28365643022300454160291628196841004894161/125944255938608020119607441810787160\) | \(125944255938608020119607441810787160\) | \([2]\) | \(5414400000\) | \(5.5873\) |
Rank
sage: E.rank()
The elliptic curves in class 338910cn have rank \(0\).
Complex multiplication
The elliptic curves in class 338910cn do not have complex multiplication.Modular form 338910.2.a.cn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.