Properties

Label 67760p
Number of curves 44
Conductor 6776067760
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 67760p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67760.bm4 67760p1 [0,0,0,5687,407286][0, 0, 0, -5687, 407286] 44851536/132055-44851536/132055 59889532890880-59889532890880 [2][2] 122880122880 1.33051.3305 Γ0(N)\Gamma_0(N)-optimal
67760.bm3 67760p2 [0,0,0,124267,16842474][0, 0, 0, -124267, 16842474] 116986321764/148225116986321764/148225 268891780326400268891780326400 [2,2][2, 2] 245760245760 1.67711.6771  
67760.bm2 67760p3 [0,0,0,158147,6929186][0, 0, 0, -158147, 6929186] 120564797922/64054375120564797922/64054375 232399324424960000232399324424960000 [2][2] 491520491520 2.02372.0237  
67760.bm1 67760p4 [0,0,0,1987667,1078607794][0, 0, 0, -1987667, 1078607794] 239369344910082/385239369344910082/385 13968404172801396840417280 [2][2] 491520491520 2.02372.0237  

Rank

sage: E.rank()
 

The elliptic curves in class 67760p have rank 00.

Complex multiplication

The elliptic curves in class 67760p do not have complex multiplication.

Modular form 67760.2.a.p

sage: E.q_eigenform(10)
 
q+q5+q73q9+2q132q17+O(q20)q + q^{5} + q^{7} - 3 q^{9} + 2 q^{13} - 2 q^{17} + 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.