Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 117600de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.hq3 117600de1 \([0, 1, 0, -7813969158, 265858972088688]\) \(448487713888272974160064/91549016015625\) \(10770650185222265625000000\) \([2, 2]\) \(123863040\) \(4.1911\) \(\Gamma_0(N)\)-optimal
117600.hq4 117600de2 \([0, 1, 0, -7787178408, 267772528198188]\) \(-55486311952875723077768/801237030029296875\) \(-754117882767333984375000000000\) \([2]\) \(247726080\) \(4.5377\)  
117600.hq2 117600de3 \([0, 1, 0, -7840766033, 263943665448063]\) \(7079962908642659949376/100085966990454375\) \(753600891549437872920000000000\) \([2]\) \(247726080\) \(4.5377\)  
117600.hq1 117600de4 \([0, 1, 0, -125023500408, 17015100987713688]\) \(229625675762164624948320008/9568125\) \(9005442705000000000\) \([2]\) \(247726080\) \(4.5377\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 117600.2.a.de

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.