Properties

Label 6384.g
Number of curves $2$
Conductor $6384$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 6384.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6384.g1 6384x1 \([0, -1, 0, -1464, -20880]\) \(84778086457/904932\) \(3706601472\) \([2]\) \(3840\) \(0.65196\) \(\Gamma_0(N)\)-optimal
6384.g2 6384x2 \([0, -1, 0, -344, -53136]\) \(-1102302937/298433646\) \(-1222384214016\) \([2]\) \(7680\) \(0.99854\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6384.2.a.g

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.