Properties

Label 141120db
Number of curves $6$
Conductor $141120$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("db1")
 
E.isogeny_class()
 

Elliptic curves in class 141120db

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.z5 141120db1 \([0, 0, 0, -27048, -7043848]\) \(-24918016/229635\) \(-20167580872535040\) \([2]\) \(786432\) \(1.8110\) \(\Gamma_0(N)\)-optimal
141120.z4 141120db2 \([0, 0, 0, -741468, -245088592]\) \(32082281296/99225\) \(139430188748390400\) \([2, 2]\) \(1572864\) \(2.1576\)  
141120.z3 141120db3 \([0, 0, 0, -1058988, -14823088]\) \(23366901604/13505625\) \(75911991651901440000\) \([2, 2]\) \(3145728\) \(2.5042\)  
141120.z1 141120db4 \([0, 0, 0, -11854668, -15710217712]\) \(32779037733124/315\) \(1770542079344640\) \([2]\) \(3145728\) \(2.5042\)  
141120.z2 141120db5 \([0, 0, 0, -11431308, 14825892368]\) \(14695548366242/57421875\) \(645510133094400000000\) \([2]\) \(6291456\) \(2.8507\)  
141120.z6 141120db6 \([0, 0, 0, 4233012, -118546288]\) \(746185003198/432360075\) \(-4860391785499076198400\) \([2]\) \(6291456\) \(2.8507\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 141120.2.a.db

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{11} - 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.