Properties

Label 117600.em
Number of curves $4$
Conductor $117600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("em1")
 
E.isogeny_class()
 

Elliptic curves in class 117600.em

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.em1 117600dh4 \([0, 1, 0, -274808, 55356888]\) \(2438569736/21\) \(19765032000000\) \([2]\) \(786432\) \(1.7190\)  
117600.em2 117600dh3 \([0, 1, 0, -60433, -4796737]\) \(3241792/567\) \(4269246912000000\) \([2]\) \(786432\) \(1.7190\)  
117600.em3 117600dh1 \([0, 1, 0, -17558, 819888]\) \(5088448/441\) \(51883209000000\) \([2, 2]\) \(393216\) \(1.3725\) \(\Gamma_0(N)\)-optimal
117600.em4 117600dh2 \([0, 1, 0, 19192, 3833388]\) \(830584/7203\) \(-6779405976000000\) \([2]\) \(786432\) \(1.7190\)  

Rank

sage: E.rank()
 

The elliptic curves in class 117600.em have rank \(1\).

Complex multiplication

The elliptic curves in class 117600.em do not have complex multiplication.

Modular form 117600.2.a.em

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4 q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.