Properties

Label 6384c
Number of curves 44
Conductor 63846384
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 6384c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6384.f4 6384c1 [0,1,0,41,86][0, -1, 0, 41, -86] 464857088/410571464857088/410571 6569136-6569136 [2][2] 10241024 0.0043898-0.0043898 Γ0(N)\Gamma_0(N)-optimal
6384.f3 6384c2 [0,1,0,204,576][0, -1, 0, -204, -576] 3685542352/14328093685542352/1432809 366799104366799104 [2,2][2, 2] 20482048 0.342180.34218  
6384.f1 6384c3 [0,1,0,2864,58032][0, -1, 0, -2864, -58032] 2538016415428/8726132538016415428/872613 893555712893555712 [2][2] 40964096 0.688760.68876  
6384.f2 6384c4 [0,1,0,1464,21600][0, -1, 0, -1464, 21600] 339112345828/8210223339112345828/8210223 84072683528407268352 [4][4] 40964096 0.688760.68876  

Rank

sage: E.rank()
 

The elliptic curves in class 6384c have rank 00.

Complex multiplication

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

Modular form 6384.2.a.c

sage: E.q_eigenform(10)
 
qq32q5q7+q9+4q11+2q13+2q15+2q17+q19+O(q20)q - q^{3} - 2 q^{5} - q^{7} + q^{9} + 4 q^{11} + 2 q^{13} + 2 q^{15} + 2 q^{17} + q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the Cremona numbering.

(1244212242144241)\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.