Properties

Label 86640ee
Number of curves 22
Conductor 8664086640
CM no
Rank 11
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ee1")
 
E.isogeny_class()
 

Elliptic curves in class 86640ee

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86640.do2 86640ee1 [0,1,0,3445,76957][0, 1, 0, -3445, -76957] 3058794496/911253058794496/91125 134742528000134742528000 [][] 9331293312 0.912390.91239 Γ0(N)\Gamma_0(N)-optimal
86640.do1 86640ee2 [0,1,0,277045,56219677][0, 1, 0, -277045, -56219677] 1590409933520896/451590409933520896/45 6653952066539520 [][] 279936279936 1.46171.4617  

Rank

sage: E.rank()
 

The elliptic curves in class 86640ee have rank 11.

Complex multiplication

The elliptic curves in class 86640ee do not have complex multiplication.

Modular form 86640.2.a.ee

sage: E.q_eigenform(10)
 
q+q3+q52q7+q9+3q11+4q13+q15+O(q20)q + q^{3} + q^{5} - 2 q^{7} + q^{9} + 3 q^{11} + 4 q^{13} + q^{15} + 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.