Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 3840.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3840.t1 3840i2 [0,1,0,61,155][0, 1, 0, -61, 155] 778688/45778688/45 14745601474560 [2][2] 512512 0.062445-0.062445  
3840.t2 3840i1 [0,1,0,11,15][0, 1, 0, -11, -15] 314432/75314432/75 3840038400 [2][2] 256256 0.40902-0.40902 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3840.2.a.t

sage: E.q_eigenform(10)
 
q+q3q5+2q7+q9+2q11+2q13q15+O(q20)q + q^{3} - q^{5} + 2 q^{7} + q^{9} + 2 q^{11} + 2 q^{13} - q^{15} + 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.