Properties

Label 16758.i
Number of curves $4$
Conductor $16758$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 16758.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16758.i1 16758g3 \([1, -1, 0, -188757, -31517375]\) \(8671983378625/82308\) \(7059237887268\) \([2]\) \(82944\) \(1.6278\)  
16758.i2 16758g4 \([1, -1, 0, -184347, -33063521]\) \(-8078253774625/846825858\) \(-72628969003156818\) \([2]\) \(165888\) \(1.9743\)  
16758.i3 16758g1 \([1, -1, 0, -3537, 7069]\) \(57066625/32832\) \(2815873284672\) \([2]\) \(27648\) \(1.0785\) \(\Gamma_0(N)\)-optimal
16758.i4 16758g2 \([1, -1, 0, 14103, 45877]\) \(3616805375/2105352\) \(-180567874379592\) \([2]\) \(55296\) \(1.4250\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16758.i have rank \(1\).

Complex multiplication

The elliptic curves in class 16758.i do not have complex multiplication.

Modular form 16758.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{8} + 4 q^{13} + q^{16} + 6 q^{17} - q^{19} + O(q^{20})\) 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.