Properties

Label 61893l
Number of curves $4$
Conductor $61893$
CM no
Rank $0$
Graph

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Show commands: 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)
 
\(q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 3 q^{8} - 2 q^{10} + 4 q^{11} + q^{13} - 4 q^{14} - q^{16} + 2 q^{17} + O(q^{20})\) Copy content Toggle raw display

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.