Properties

Label 103488.ce
Number of curves $4$
Conductor $103488$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ce1")
 
E.isogeny_class()
 

Elliptic curves in class 103488.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
103488.ce1 103488fc4 \([0, -1, 0, -44321153, -113547531999]\) \(312196988566716625/25367712678\) \(782365105547908743168\) \([2]\) \(5308416\) \(3.0542\)  
103488.ce2 103488fc3 \([0, -1, 0, -2580993, -2026172511]\) \(-61653281712625/21875235228\) \(-674653680261915475968\) \([2]\) \(2654208\) \(2.7077\)  
103488.ce3 103488fc2 \([0, -1, 0, -1138433, 234870945]\) \(5290763640625/2291573592\) \(70674374072784125952\) \([2]\) \(1769472\) \(2.5049\)  
103488.ce4 103488fc1 \([0, -1, 0, 241407, 27067041]\) \(50447927375/39517632\) \(-1218762476661768192\) \([2]\) \(884736\) \(2.1584\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 103488.ce have rank \(1\).

Complex multiplication

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

Modular form 103488.2.a.ce

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.