Properties

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

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Show commands: SageMath
E = EllipticCurve("on1")
 
E.isogeny_class()
 

Elliptic curves in class 141120.on

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.on1 141120jw2 \([0, 0, 0, -13858572, -19858344464]\) \(-5452947409/250\) \(-13495465182560256000\) \([]\) \(5806080\) \(2.7464\)  
141120.on2 141120jw1 \([0, 0, 0, -28812, -70723856]\) \(-49/40\) \(-2159274429209640960\) \([]\) \(1935360\) \(2.1971\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.on

sage: E.q_eigenform(10)
 
\(q + q^{5} + 3 q^{11} + 5 q^{13} + 6 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.