Properties

Label 1920.t
Number of curves 22
Conductor 19201920
CM no
Rank 11
Graph

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

Elliptic curves in class 1920.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1920.t1 1920i2 [0,1,0,1225,15623][0, 1, 0, -1225, 15623] 24836849888/82012524836849888/820125 67184640006718464000 [2][2] 15361536 0.658830.65883  
1920.t2 1920i1 [0,1,0,25,873][0, 1, 0, 25, 873] 6483584/12656256483584/1265625 324000000-324000000 [2][2] 768768 0.312260.31226 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1920.t have rank 11.

Complex multiplication

The elliptic curves in class 1920.t do not have complex multiplication.

Modular form 1920.2.a.t

sage: E.q_eigenform(10)
 
q+q3+q52q7+q92q116q13+q156q17+6q19+O(q20)q + q^{3} + q^{5} - 2 q^{7} + q^{9} - 2 q^{11} - 6 q^{13} + q^{15} - 6 q^{17} + 6 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.