Properties

Label 28560dh
Number of curves $2$
Conductor $28560$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28560dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28560.cj2 28560dh1 \([0, 1, 0, 1304, -21196]\) \(59822347031/83966400\) \(-343926374400\) \([2]\) \(27648\) \(0.89927\) \(\Gamma_0(N)\)-optimal
28560.cj1 28560dh2 \([0, 1, 0, -8296, -217036]\) \(15417797707369/4080067320\) \(16711955742720\) \([2]\) \(55296\) \(1.2458\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28560dh have rank \(0\).

Complex multiplication

The elliptic curves in class 28560dh do not have complex multiplication.

Modular form 28560.2.a.dh

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} - 2q^{11} - 2q^{13} - q^{15} + q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.