Properties

Label 3168.v
Number of curves 22
Conductor 31683168
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 3168.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3168.v1 3168e1 [0,0,0,1329,18648][0, 0, 0, -1329, -18648] 150229394496/1331150229394496/1331 22999682299968 [2][2] 768768 0.386890.38689 Γ0(N)\Gamma_0(N)-optimal
3168.v2 3168e2 [0,0,0,1299,19530][0, 0, 0, -1299, -19530] 17535471192/1771561-17535471192/1771561 24490059264-24490059264 [2][2] 15361536 0.733470.73347  

Rank

sage: E.rank()
 

The elliptic curves in class 3168.v have rank 00.

Complex multiplication

The elliptic curves in class 3168.v do not have complex multiplication.

Modular form 3168.2.a.v

sage: E.q_eigenform(10)
 
q+2q5+q112q17+6q19+O(q20)q + 2 q^{5} + q^{11} - 2 q^{17} + 6 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.

(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 LMFDB labels.