Properties

Label 4680e
Number of curves 22
Conductor 46804680
CM no
Rank 11
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 4680e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4680.e1 4680e1 [0,0,0,183,938][0, 0, 0, -183, 938] 3631696/653631696/65 1213056012130560 [2][2] 768768 0.154970.15497 Γ0(N)\Gamma_0(N)-optimal
4680.e2 4680e2 [0,0,0,3,2702][0, 0, 0, -3, 2702] 4/4225-4/4225 3153945600-3153945600 [2][2] 15361536 0.501540.50154  

Rank

sage: E.rank()
 

The elliptic curves in class 4680e have rank 11.

Complex multiplication

The elliptic curves in class 4680e do not have complex multiplication.

Modular form 4680.2.a.e

sage: E.q_eigenform(10)
 
qq52q11+q132q17+2q19+O(q20)q - q^{5} - 2 q^{11} + q^{13} - 2 q^{17} + 2 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.