Properties

Label 141120.c
Number of curves 22
Conductor 141120141120
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.c1 141120oy2 [0,0,0,94668,11025392][0, 0, 0, -94668, 11025392] 1314036/251314036/25 17851144421376001785114442137600 [2][2] 917504917504 1.71991.7199  
141120.c2 141120oy1 [0,0,0,12348,268912][0, 0, 0, -12348, -268912] 11664/511664/5 8925572210688089255722106880 [2][2] 458752458752 1.37331.3733 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 141120.c have rank 00.

Complex multiplication

The elliptic curves in class 141120.c do not have complex multiplication.

Modular form 141120.2.a.c

sage: E.q_eigenform(10)
 
qq56q112q132q17+6q19+O(q20)q - q^{5} - 6 q^{11} - 2 q^{13} - 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.