Properties

Label 4928.g
Number of curves 22
Conductor 49284928
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 4928.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4928.g1 4928e2 [0,1,0,3297,66175][0, 1, 0, -3297, 66175] 15124197817/129413915124197817/1294139 339250774016339250774016 [2][2] 61446144 0.953700.95370  
4928.g2 4928e1 [0,1,0,223,4927][0, 1, 0, 223, 4927] 4657463/415034657463/41503 10879762432-10879762432 [2][2] 30723072 0.607130.60713 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4928.g have rank 11.

Complex multiplication

The elliptic curves in class 4928.g do not have complex multiplication.

Modular form 4928.2.a.g

sage: E.q_eigenform(10)
 
q2q3+2q5q7+q9q114q134q15+4q17+O(q20)q - 2 q^{3} + 2 q^{5} - q^{7} + q^{9} - q^{11} - 4 q^{13} - 4 q^{15} + 4 q^{17} + 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.