Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("kc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120kc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.oy2 141120kc1 \([0, 0, 0, 1428, -22736]\) \(19652/25\) \(-409677004800\) \([2]\) \(147456\) \(0.91420\) \(\Gamma_0(N)\)-optimal
141120.oy1 141120kc2 \([0, 0, 0, -8652, -220304]\) \(2185454/625\) \(20483850240000\) \([2]\) \(294912\) \(1.2608\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.kc

sage: E.q_eigenform(10)
 
\(q + q^{5} + 4 q^{11} - 2 q^{13} - 2 q^{19} + O(q^{20})\) 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 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.