Properties

Label 89280do
Number of curves 22
Conductor 8928089280
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 89280do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
89280.fb1 89280do1 [0,0,0,45612,4402736][0, 0, 0, -45612, -4402736] 1482713947827/325058560-1482713947827/325058560 2300728081121280-2300728081121280 [][] 387072387072 1.66841.6684 Γ0(N)\Gamma_0(N)-optimal
89280.fb2 89280do2 [0,0,0,323028,26448336][0, 0, 0, 323028, 26448336] 722458663317/476656000722458663317/476656000 2459440263462912000-2459440263462912000 [][] 11612161161216 2.21772.2177  

Rank

sage: E.rank()
 

The elliptic curves in class 89280do have rank 11.

Complex multiplication

The elliptic curves in class 89280do do not have complex multiplication.

Modular form 89280.2.a.do

sage: E.q_eigenform(10)
 
q+q5+q7+3q11+4q136q17q19+O(q20)q + q^{5} + q^{7} + 3 q^{11} + 4 q^{13} - 6 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.

(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.