Properties

Label 3840.b
Number of curves 22
Conductor 38403840
CM no
Rank 00
Graph

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

Elliptic curves in class 3840.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3840.b1 3840q2 [0,1,0,23661,1407861][0, -1, 0, -23661, 1407861] 44708635815488/3417187544708635815488/34171875 11197440000001119744000000 [2][2] 1075210752 1.24421.2442  
3840.b2 3840q1 [0,1,0,1791,12555][0, -1, 0, -1791, 12555] 1241603628992/5978711251241603628992/597871125 306110016000306110016000 [2][2] 53765376 0.897630.89763 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3840.b have rank 00.

Complex multiplication

The elliptic curves in class 3840.b do not have complex multiplication.

Modular form 3840.2.a.b

sage: E.q_eigenform(10)
 
qq3q52q7+q92q11+2q13+q158q17+8q19+O(q20)q - q^{3} - q^{5} - 2 q^{7} + q^{9} - 2 q^{11} + 2 q^{13} + q^{15} - 8 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.