Properties

Label 141120ek
Number of curves $4$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ek1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.gn4 141120ek1 \([0, 0, 0, -705668943, -7126549533992]\) \(7079962908642659949376/100085966990454375\) \(549375049939540209358680000\) \([2]\) \(82575360\) \(3.9357\) \(\Gamma_0(N)\)-optimal
141120.gn2 141120ek2 \([0, 0, 0, -11252115588, -459408804615488]\) \(448487713888272974160064/91549016015625\) \(32160989122670721600000000\) \([2, 2]\) \(165150720\) \(4.2822\)  
141120.gn3 141120ek3 \([0, 0, 0, -11213536908, -462715414141232]\) \(-55486311952875723077768/801237030029296875\) \(-2251783932057135000000000000000\) \([2]\) \(330301440\) \(4.6288\)  
141120.gn1 141120ek4 \([0, 0, 0, -180033840588, -29402166520305488]\) \(229625675762164624948320008/9568125\) \(26890107830046720000\) \([2]\) \(330301440\) \(4.6288\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141120ek have rank \(0\).

Complex multiplication

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

Modular form 141120.2.a.ek

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.