Properties

Label 17328f
Number of curves $6$
Conductor $17328$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17328f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17328.d5 17328f1 \([0, -1, 0, 241, 1698]\) \(2048/3\) \(-2258202288\) \([2]\) \(6912\) \(0.48029\) \(\Gamma_0(N)\)-optimal
17328.d4 17328f2 \([0, -1, 0, -1564, 18304]\) \(35152/9\) \(108393709824\) \([2, 2]\) \(13824\) \(0.82687\)  
17328.d3 17328f3 \([0, -1, 0, -8784, -299376]\) \(1556068/81\) \(3902173553664\) \([2, 2]\) \(27648\) \(1.1734\)  
17328.d2 17328f4 \([0, -1, 0, -23224, 1369888]\) \(28756228/3\) \(144524946432\) \([2]\) \(27648\) \(1.1734\)  
17328.d1 17328f5 \([0, -1, 0, -138744, -19845360]\) \(3065617154/9\) \(867149678592\) \([2]\) \(55296\) \(1.5200\)  
17328.d6 17328f6 \([0, -1, 0, 5656, -1200432]\) \(207646/6561\) \(-632152115693568\) \([2]\) \(55296\) \(1.5200\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17328f have rank \(0\).

Complex multiplication

The elliptic curves in class 17328f do not have complex multiplication.

Modular form 17328.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{5} + q^{9} - 4q^{11} + 2q^{13} + 2q^{15} + 2q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.