Properties

Label 141120p
Number of curves $2$
Conductor $141120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 141120p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.kf1 141120p1 \([0, 0, 0, -8652, -118384]\) \(1092727/540\) \(35396093214720\) \([2]\) \(294912\) \(1.2929\) \(\Gamma_0(N)\)-optimal
141120.kf2 141120p2 \([0, 0, 0, 31668, -908656]\) \(53582633/36450\) \(-2389236291993600\) \([2]\) \(589824\) \(1.6395\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141120p have rank \(1\).

Complex multiplication

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

Modular form 141120.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2 q^{11} - 2 q^{13} + 4 q^{17} + O(q^{20})\) 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 Cremona 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 Cremona labels.