Properties

Label 56784v
Number of curves $4$
Conductor $56784$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 56784v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56784.ce4 56784v1 \([0, 1, 0, -1239, -109368]\) \(-2725888/64827\) \(-5006520752688\) \([2]\) \(92160\) \(1.1175\) \(\Gamma_0(N)\)-optimal
56784.ce3 56784v2 \([0, 1, 0, -42644, -3388644]\) \(6940769488/35721\) \(44139121737984\) \([2, 2]\) \(184320\) \(1.4641\)  
56784.ce2 56784v3 \([0, 1, 0, -66304, 766052]\) \(6522128932/3720087\) \(18387096998280192\) \([2]\) \(368640\) \(1.8107\)  
56784.ce1 56784v4 \([0, 1, 0, -681464, -216754524]\) \(7080974546692/189\) \(934161306624\) \([2]\) \(368640\) \(1.8107\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56784v have rank \(1\).

Complex multiplication

The elliptic curves in class 56784v do not have complex multiplication.

Modular form 56784.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{7} + q^{9} - 2 q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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.