Properties

Label 158400.oy
Number of curves $2$
Conductor $158400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("oy1")
 
E.isogeny_class()
 

Elliptic curves in class 158400.oy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.oy1 158400fw1 \([0, 0, 0, -1274700, 559226000]\) \(-76711450249/851840\) \(-2543580610560000000\) \([]\) \(3870720\) \(2.3466\) \(\Gamma_0(N)\)-optimal
158400.oy2 158400fw2 \([0, 0, 0, 4269300, 2898794000]\) \(2882081488391/2883584000\) \(-8610335686656000000000\) \([]\) \(11612160\) \(2.8959\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 158400.2.a.oy

sage: E.q_eigenform(10)
 
\(q + 5 q^{7} - q^{11} + 2 q^{13} + 3 q^{17} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.