Properties

Label 46893n
Number of curves $4$
Conductor $46893$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 46893n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46893.p3 46893n1 \([1, 0, 1, -2427, -45671]\) \(13430356633/180873\) \(21279527577\) \([2]\) \(39936\) \(0.78841\) \(\Gamma_0(N)\)-optimal
46893.p2 46893n2 \([1, 0, 1, -4632, 49585]\) \(93391282153/44876601\) \(5279687231049\) \([2, 2]\) \(79872\) \(1.1350\)  
46893.p4 46893n3 \([1, 0, 1, 16683, 382099]\) \(4365111505607/3058314567\) \(-359807650492983\) \([2]\) \(159744\) \(1.4816\)  
46893.p1 46893n4 \([1, 0, 1, -61227, 5822275]\) \(215751695207833/163381911\) \(19221718447239\) \([2]\) \(159744\) \(1.4816\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46893n have rank \(0\).

Complex multiplication

The elliptic curves in class 46893n do not have complex multiplication.

Modular form 46893.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} - 3 q^{8} + q^{9} - 2 q^{10} + q^{11} - q^{12} + 2 q^{13} - 2 q^{15} - q^{16} + 2 q^{17} + q^{18} + O(q^{20})\) 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.