Properties

Label 29988.t
Number of curves 22
Conductor 2998829988
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 29988.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29988.t1 29988t2 [0,0,0,17275440,27637166788][0, 0, 0, -17275440, 27637166788] 1272481306550272000/5865429267-1272481306550272000/5865429267 2628206321530583808-2628206321530583808 [3][3] 881280881280 2.73772.7377  
29988.t2 29988t1 [0,0,0,129360,67984756][0, 0, 0, -129360, 67984756] 534274048000/4146834123-534274048000/4146834123 1858130950061175552-1858130950061175552 [][] 293760293760 2.18842.1884 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 29988.t have rank 00.

Complex multiplication

The elliptic curves in class 29988.t do not have complex multiplication.

Modular form 29988.2.a.t

sage: E.q_eigenform(10)
 
q+5q13+q17q19+O(q20)q + 5 q^{13} + 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 LMFDB 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 LMFDB labels.