Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("hh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 141120.hh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.hh1 141120eq3 \([0, 0, 0, -1976268, 1069342288]\) \(303735479048/105\) \(295090346557440\) \([2]\) \(2359296\) \(2.1324\)  
141120.hh2 141120eq2 \([0, 0, 0, -124068, 16551808]\) \(601211584/11025\) \(3873060798566400\) \([2, 2]\) \(1179648\) \(1.7858\)  
141120.hh3 141120eq1 \([0, 0, 0, -16023, -389648]\) \(82881856/36015\) \(197687478260160\) \([2]\) \(589824\) \(1.4393\) \(\Gamma_0(N)\)-optimal
141120.hh4 141120eq4 \([0, 0, 0, -588, 48014512]\) \(-8/354375\) \(-995929919631360000\) \([2]\) \(2359296\) \(2.1324\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.hh

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 LMFDB 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 LMFDB labels.