Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 117600dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.hz3 117600dd1 \([0, 1, 0, -86158, -9607312]\) \(601211584/11025\) \(1297080225000000\) \([2, 2]\) \(884736\) \(1.6947\) \(\Gamma_0(N)\)-optimal
117600.hz4 117600dd2 \([0, 1, 0, -408, -27786312]\) \(-8/354375\) \(-333534915000000000\) \([2]\) \(1769472\) \(2.0413\)  
117600.hz2 117600dd3 \([0, 1, 0, -178033, 14372063]\) \(82881856/36015\) \(271176239040000000\) \([2]\) \(1769472\) \(2.0413\)  
117600.hz1 117600dd4 \([0, 1, 0, -1372408, -619289812]\) \(303735479048/105\) \(98825160000000\) \([2]\) \(1769472\) \(2.0413\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 117600.2.a.dd

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.