Properties

Label 406.a
Number of curves 22
Conductor 406406
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 406.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
406.a1 406a2 [1,1,0,4942,134964][1, -1, 0, -4942, 134964] 13350003080765625/10917827213350003080765625/109178272 109178272109178272 [2][2] 240240 0.713090.71309  
406.a2 406a1 [1,1,0,302,2260][1, -1, 0, -302, 2260] 3051779837625/295386112-3051779837625/295386112 295386112-295386112 [2][2] 120120 0.366510.36651 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 406.a have rank 11.

Complex multiplication

The elliptic curves in class 406.a do not have complex multiplication.

Modular form 406.2.a.a

sage: E.q_eigenform(10)
 
qq2+q4q7q83q94q11+q14+q164q17+3q18+4q19+O(q20)q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} - 4 q^{11} + q^{14} + q^{16} - 4 q^{17} + 3 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.