Properties

Label 141120.ln
Number of curves 44
Conductor 141120141120
CM no
Rank 00
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ln1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.ln

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.ln1 141120jb4 [0,0,0,381612,90678224][0, 0, 0, -381612, -90678224] 546718898/405546718898/405 45528224897433604552822489743360 [2][2] 11796481179648 1.93821.9382  
141120.ln2 141120jb3 [0,0,0,240492,44853424][0, 0, 0, -240492, 44853424] 136835858/1875136835858/1875 2107788189696000021077881896960000 [2][2] 11796481179648 1.93821.9382  
141120.ln3 141120jb2 [0,0,0,28812,784784][0, 0, 0, -28812, -784784] 470596/225470596/225 12646729138176001264672913817600 [2,2][2, 2] 589824589824 1.59171.5917  
141120.ln4 141120jb1 [0,0,0,6468,93296][0, 0, 0, 6468, -93296] 21296/1521296/15 21077881896960-21077881896960 [2][2] 294912294912 1.24511.2451 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.ln

sage: E.q_eigenform(10)
 
q+q56q132q17+4q19+O(q20)q + q^{5} - 6 q^{13} - 2 q^{17} + 4 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.

(1424412422124421)\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.