Properties

Label 110670.cg
Number of curves 22
Conductor 110670110670
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 110670.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110670.cg1 110670ci1 [1,0,0,108511,13767115][1, 0, 0, -108511, -13767115] 141301007904351819889/488164263300141301007904351819889/488164263300 488164263300488164263300 [2][2] 497664497664 1.46271.4627 Γ0(N)\Gamma_0(N)-optimal
110670.cg2 110670ci2 [1,0,0,106981,14173789][1, 0, 0, -106981, -14173789] 135407875813098709969/8317018870571250-135407875813098709969/8317018870571250 8317018870571250-8317018870571250 [2][2] 995328995328 1.80931.8093  

Rank

sage: E.rank()
 

The elliptic curves in class 110670.cg have rank 00.

Complex multiplication

The elliptic curves in class 110670.cg do not have complex multiplication.

Modular form 110670.2.a.cg

sage: E.q_eigenform(10)
 
q+q2+q3+q4q5+q6+q7+q8+q9q10+2q11+q12+6q13+q14q15+q16+q17+q184q19+O(q20)q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} + 2 q^{11} + q^{12} + 6 q^{13} + q^{14} - q^{15} + q^{16} + q^{17} + q^{18} - 4 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.