Properties

Label 6384.v
Number of curves $4$
Conductor $6384$
CM no
Rank $1$
Graph

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

Elliptic curves in class 6384.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6384.v1 6384n3 \([0, 1, 0, -592824, -175883580]\) \(22501000029889239268/3620708343\) \(3707605343232\) \([2]\) \(49152\) \(1.8142\)  
6384.v2 6384n2 \([0, 1, 0, -37164, -2739924]\) \(22174957026242512/278654127129\) \(71335456545024\) \([2, 2]\) \(24576\) \(1.4676\)  
6384.v3 6384n4 \([0, 1, 0, -6384, -7110684]\) \(-28104147578308/21301741002339\) \(-21812982786395136\) \([4]\) \(49152\) \(1.8142\)  
6384.v4 6384n1 \([0, 1, 0, -4359, 41940]\) \(572616640141312/280535480757\) \(4488567692112\) \([2]\) \(12288\) \(1.1210\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6384.v have rank \(1\).

Complex multiplication

The elliptic curves in class 6384.v do not have complex multiplication.

Modular form 6384.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{7} + q^{9} + 4 q^{11} + 2 q^{13} - 2 q^{15} - 6 q^{17} - q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.