Properties

Label 117600.en
Number of curves $4$
Conductor $117600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("en1")
 
E.isogeny_class()
 

Elliptic curves in class 117600.en

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.en1 117600hh4 \([0, 1, 0, -388963633, -2952777215137]\) \(864335783029582144/59535\) \(448270925760000000\) \([2]\) \(17694720\) \(3.2879\)  
117600.en2 117600hh3 \([0, 1, 0, -27313008, -34030077012]\) \(2394165105226952/854262178245\) \(804024728066768040000000\) \([2]\) \(17694720\) \(3.2879\)  
117600.en3 117600hh1 \([0, 1, 0, -24311758, -46137119512]\) \(13507798771700416/3544416225\) \(416997024455025000000\) \([2, 2]\) \(8847360\) \(2.9414\) \(\Gamma_0(N)\)-optimal
117600.en4 117600hh2 \([0, 1, 0, -21335008, -57853607512]\) \(-1141100604753992/875529151875\) \(-824041033511535000000000\) \([2]\) \(17694720\) \(3.2879\)  

Rank

sage: E.rank()
 

The elliptic curves in class 117600.en have rank \(0\).

Complex multiplication

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

Modular form 117600.2.a.en

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