Properties

Label 103488ee
Number of curves $4$
Conductor $103488$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ee1")
 
E.isogeny_class()
 

Elliptic curves in class 103488ee

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
103488.fw4 103488ee1 \([0, 1, 0, 131, -15709]\) \(2048/891\) \(-107341065216\) \([2]\) \(110592\) \(0.79570\) \(\Gamma_0(N)\)-optimal
103488.fw3 103488ee2 \([0, 1, 0, -8689, -306769]\) \(37642192/1089\) \(2099114164224\) \([2, 2]\) \(221184\) \(1.1423\)  
103488.fw2 103488ee3 \([0, 1, 0, -20449, 688127]\) \(122657188/43923\) \(338657085161472\) \([2]\) \(442368\) \(1.4888\)  
103488.fw1 103488ee4 \([0, 1, 0, -138049, -19788385]\) \(37736227588/33\) \(254438080512\) \([2]\) \(442368\) \(1.4888\)  

Rank

sage: E.rank()
 

The elliptic curves in class 103488ee have rank \(0\).

Complex multiplication

The elliptic curves in class 103488ee do not have complex multiplication.

Modular form 103488.2.a.ee

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{9} + q^{11} + 6 q^{13} - 2 q^{15} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.