Properties

Label 239400.ej
Number of curves $4$
Conductor $239400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ej1")
 
E.isogeny_class()
 

Elliptic curves in class 239400.ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
239400.ej1 239400ej3 \([0, 0, 0, -727275, 198103750]\) \(1823652903746/328593657\) \(7665432830496000000\) \([2]\) \(5242880\) \(2.3426\)  
239400.ej2 239400ej2 \([0, 0, 0, -214275, -35311250]\) \(93280467172/7800849\) \(90989102736000000\) \([2, 2]\) \(2621440\) \(1.9960\)  
239400.ej3 239400ej1 \([0, 0, 0, -209775, -36980750]\) \(350104249168/2793\) \(8144388000000\) \([2]\) \(1310720\) \(1.6495\) \(\Gamma_0(N)\)-optimal
239400.ej4 239400ej4 \([0, 0, 0, 226725, -161878250]\) \(55251546334/517244049\) \(-12066269175072000000\) \([2]\) \(5242880\) \(2.3426\)  

Rank

sage: E.rank()
 

The elliptic curves in class 239400.ej have rank \(0\).

Complex multiplication

The elliptic curves in class 239400.ej do not have complex multiplication.

Modular form 239400.2.a.ej

sage: E.q_eigenform(10)
 
\(q + q^{7} + 4 q^{11} + 6 q^{13} + 2 q^{17} - q^{19} + O(q^{20})\) 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.