Properties

Label 19110f
Number of curves 22
Conductor 1911019110
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 19110f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19110.k1 19110f1 [1,1,0,6052,189986][1, 1, 0, -6052, -189986] 86806489/3510-86806489/3510 991488123990-991488123990 [][] 3628836288 1.06981.0698 Γ0(N)\Gamma_0(N)-optimal
19110.k2 19110f2 [1,1,0,29963,557339][1, 1, 0, 29963, -557339] 10531168151/659100010531168151/6591000 1861794366159000-1861794366159000 [][] 108864108864 1.61911.6191  

Rank

sage: E.rank()
 

The elliptic curves in class 19110f have rank 11.

Complex multiplication

The elliptic curves in class 19110f do not have complex multiplication.

Modular form 19110.2.a.f

sage: E.q_eigenform(10)
 
qq2q3+q4+q5+q6q8+q9q10q12q13q15+q16+3q17q18+q19+O(q20)q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - q^{15} + q^{16} + 3 q^{17} - q^{18} + 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 Cremona numbering.

(1331)\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.