Properties

Label 9200v
Number of curves 22
Conductor 92009200
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 9200v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9200.h2 9200v1 [0,1,0,2708,53912][0, 1, 0, -2708, -53912] 878800/23878800/23 5750000000057500000000 [][] 1008010080 0.846120.84612 Γ0(N)\Gamma_0(N)-optimal
9200.h1 9200v2 [0,1,0,27708,1746088][0, 1, 0, -27708, 1746088] 941054800/12167941054800/12167 3041750000000030417500000000 [][] 3024030240 1.39541.3954  

Rank

sage: E.rank()
 

The elliptic curves in class 9200v have rank 00.

Complex multiplication

The elliptic curves in class 9200v do not have complex multiplication.

Modular form 9200.2.a.v

sage: E.q_eigenform(10)
 
q2q3q7+q9+3q115q136q17+7q19+O(q20)q - 2 q^{3} - q^{7} + q^{9} + 3 q^{11} - 5 q^{13} - 6 q^{17} + 7 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.