Properties

Label 264.b
Number of curves 44
Conductor 264264
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 264.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
264.b1 264c4 [0,1,0,704,6960][0, 1, 0, -704, 6960] 37736227588/3337736227588/33 3379233792 [2][2] 9696 0.169320.16932  
264.b2 264c3 [0,1,0,104,288][0, 1, 0, -104, -288] 122657188/43923122657188/43923 4497715244977152 [2][2] 9696 0.169320.16932  
264.b3 264c2 [0,1,0,44,96][0, 1, 0, -44, 96] 37642192/108937642192/1089 278784278784 [2,2][2, 2] 4848 0.17725-0.17725  
264.b4 264c1 [0,1,0,1,6][0, 1, 0, 1, 6] 2048/8912048/891 14256-14256 [4][4] 2424 0.52383-0.52383 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 264.b have rank 00.

Complex multiplication

The elliptic curves in class 264.b do not have complex multiplication.

Modular form 264.2.a.b

sage: E.q_eigenform(10)
 
q+q32q5+4q7+q9q11+6q132q15+6q178q19+O(q20)q + q^{3} - 2 q^{5} + 4 q^{7} + q^{9} - q^{11} + 6 q^{13} - 2 q^{15} + 6 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.

(1424412422124421)\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.