Properties

Label 158400.s
Number of curves $4$
Conductor $158400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 158400.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.s1 158400ke3 \([0, 0, 0, -1454700, 641486000]\) \(228027144098/12890625\) \(19245600000000000000\) \([2]\) \(4718592\) \(2.4549\)  
158400.s2 158400ke2 \([0, 0, 0, -266700, -40426000]\) \(2810381476/680625\) \(508083840000000000\) \([2, 2]\) \(2359296\) \(2.1084\)  
158400.s3 158400ke1 \([0, 0, 0, -248700, -47734000]\) \(9115564624/825\) \(153964800000000\) \([2]\) \(1179648\) \(1.7618\) \(\Gamma_0(N)\)-optimal
158400.s4 158400ke4 \([0, 0, 0, 633300, -254626000]\) \(18814587262/29648025\) \(-44264264140800000000\) \([2]\) \(4718592\) \(2.4549\)  

Rank

sage: E.rank()
 

The elliptic curves in class 158400.s have rank \(0\).

Complex multiplication

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

Modular form 158400.2.a.s

sage: E.q_eigenform(10)
 
\(q - 4 q^{7} - q^{11} + 2 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 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.