Properties

Label 384.d
Number of curves 22
Conductor 384384
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 384.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
384.d1 384f2 [0,1,0,141,693][0, -1, 0, -141, 693] 19056256/2719056256/27 442368442368 [2][2] 9696 0.013528-0.013528  
384.d2 384f1 [0,1,0,6,18][0, -1, 0, -6, 18] 219488/729-219488/729 93312-93312 [2][2] 4848 0.36010-0.36010 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 384.d have rank 00.

Complex multiplication

The elliptic curves in class 384.d do not have complex multiplication.

Modular form 384.2.a.d

sage: E.q_eigenform(10)
 
qq3+4q52q7+q9+4q112q134q152q17+8q19+O(q20)q - q^{3} + 4 q^{5} - 2 q^{7} + q^{9} + 4 q^{11} - 2 q^{13} - 4 q^{15} - 2 q^{17} + 8 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 LMFDB numbering.

(1221)\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.