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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 61893l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61893.d4 | 61893l1 | \([1, -1, 1, 2281, -89922]\) | \(12167/39\) | \(-4208808360159\) | \([2]\) | \(101376\) | \(1.1055\) | \(\Gamma_0(N)\)-optimal |
61893.d3 | 61893l2 | \([1, -1, 1, -21524, -1042122]\) | \(10218313/1521\) | \(164143526046201\) | \([2, 2]\) | \(202752\) | \(1.4521\) | |
61893.d2 | 61893l3 | \([1, -1, 1, -92939, 9898656]\) | \(822656953/85683\) | \(9246751967269323\) | \([2]\) | \(405504\) | \(1.7987\) | |
61893.d1 | 61893l4 | \([1, -1, 1, -330989, -73209360]\) | \(37159393753/1053\) | \(113637825724293\) | \([2]\) | \(405504\) | \(1.7987\) |
Rank
sage: E.rank()
The elliptic curves in class 61893l have rank \(0\).
Complex multiplication
The elliptic curves in class 61893l do not have complex multiplication.Modular form 61893.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.