Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 9200.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9200.bh1 9200bi2 [0,1,0,1108,14412][0, -1, 0, -1108, 14412] 941054800/12167941054800/12167 19467200001946720000 [][] 60486048 0.590710.59071  
9200.bh2 9200bi1 [0,1,0,108,388][0, -1, 0, -108, -388] 878800/23878800/23 36800003680000 [][] 20162016 0.0414060.041406 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9200.bh have rank 00.

Complex multiplication

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

Modular form 9200.2.a.bh

sage: E.q_eigenform(10)
 
q+2q3+q7+q9+3q11+5q13+6q17+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 LMFDB 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 LMFDB labels.