Properties

Label 158400eg
Number of curves $4$
Conductor $158400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eg1")
 
E.isogeny_class()
 

Elliptic curves in class 158400eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.hj3 158400eg1 \([0, 0, 0, -11100, -434000]\) \(810448/33\) \(6158592000000\) \([2]\) \(262144\) \(1.2199\) \(\Gamma_0(N)\)-optimal
158400.hj2 158400eg2 \([0, 0, 0, -29100, 1330000]\) \(3650692/1089\) \(812934144000000\) \([2, 2]\) \(524288\) \(1.5664\)  
158400.hj1 158400eg3 \([0, 0, 0, -425100, 106666000]\) \(5690357426/891\) \(1330255872000000\) \([2]\) \(1048576\) \(1.9130\)  
158400.hj4 158400eg4 \([0, 0, 0, 78900, 8890000]\) \(36382894/43923\) \(-65576687616000000\) \([2]\) \(1048576\) \(1.9130\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158400eg have rank \(1\).

Complex multiplication

The elliptic curves in class 158400eg do not have complex multiplication.

Modular form 158400.2.a.eg

sage: E.q_eigenform(10)
 
\(q - q^{11} + 2 q^{13} + 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.