Properties

Label 178752bq
Number of curves 22
Conductor 178752178752
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("bq1")
 
E.isogeny_class()
 

Elliptic curves in class 178752bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
178752.hv2 178752bq1 [0,1,0,48347,4318693][0, 1, 0, 48347, -4318693] 103737344000/127413867103737344000/127413867 15349876775611392-15349876775611392 [2][2] 13271041327104 1.79191.7919 Γ0(N)\Gamma_0(N)-optimal
178752.hv1 178752bq2 [0,1,0,287793,41764689][0, 1, 0, -287793, -41764689] 1367595682000/4023009271367595682000/402300927 775459664046047232775459664046047232 [2][2] 26542082654208 2.13852.1385  

Rank

sage: E.rank()
 

The elliptic curves in class 178752bq have rank 00.

Complex multiplication

The elliptic curves in class 178752bq do not have complex multiplication.

Modular form 178752.2.a.bq

sage: E.q_eigenform(10)
 
q+q3+q92q11+6q13+8q17q19+O(q20)q + q^{3} + q^{9} - 2 q^{11} + 6 q^{13} + 8 q^{17} - 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.

(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 Cremona labels.