Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6384.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6384.m1 6384u4 \([0, -1, 0, -19472, 1052352]\) \(199350693197713/547428\) \(2242265088\) \([4]\) \(6144\) \(1.0274\)  
6384.m2 6384u3 \([0, -1, 0, -3472, -57152]\) \(1130389181713/295568028\) \(1210646642688\) \([2]\) \(6144\) \(1.0274\)  
6384.m3 6384u2 \([0, -1, 0, -1232, 16320]\) \(50529889873/2547216\) \(10433396736\) \([2, 2]\) \(3072\) \(0.68083\)  
6384.m4 6384u1 \([0, -1, 0, 48, 960]\) \(2924207/102144\) \(-418381824\) \([2]\) \(1536\) \(0.33426\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6384.2.a.m

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.