Properties

Label 141120.k
Number of curves $2$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.k1 141120cv1 \([0, 0, 0, -615468, -105986608]\) \(393349474783/153600000\) \(10068222069964800000\) \([2]\) \(3440640\) \(2.3450\) \(\Gamma_0(N)\)-optimal
141120.k2 141120cv2 \([0, 0, 0, 1965012, -763492912]\) \(12801408679457/11250000000\) \(-737418608640000000000\) \([2]\) \(6881280\) \(2.6916\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{5} - 6 q^{11} + 6 q^{13} + 4 q^{19} + O(q^{20})\) Copy content 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.