Properties

Label 91260x
Number of curves 22
Conductor 9126091260
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 91260x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91260.z1 91260x1 [0,0,0,109512,13999284][0, 0, 0, -109512, 13999284] 5971968/25-5971968/25 608038921900800-608038921900800 [][] 505440505440 1.69171.6917 Γ0(N)\Gamma_0(N)-optimal
91260.z2 91260x2 [0,0,0,255528,73792836][0, 0, 0, 255528, 73792836] 8429568/156258429568/15625 3420218935692000000-3420218935692000000 [][] 15163201516320 2.24112.2411  

Rank

sage: E.rank()
 

The elliptic curves in class 91260x have rank 00.

Complex multiplication

The elliptic curves in class 91260x do not have complex multiplication.

Modular form 91260.2.a.x

sage: E.q_eigenform(10)
 
q+q5+q7+6q11+q19+O(q20)q + q^{5} + q^{7} + 6 q^{11} + 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.