Properties

Label 321600dk
Number of curves $2$
Conductor $321600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dk1")
 
E.isogeny_class()
 

Elliptic curves in class 321600dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
321600.dk2 321600dk1 \([0, -1, 0, 23867, -223613]\) \(1503484706816/890163675\) \(-890163675000000\) \([]\) \(1658880\) \(1.5579\) \(\Gamma_0(N)\)-optimal
321600.dk1 321600dk2 \([0, -1, 0, -300133, 70003387]\) \(-2989967081734144/380653171875\) \(-380653171875000000\) \([]\) \(4976640\) \(2.1072\)  

Rank

sage: E.rank()
 

The elliptic curves in class 321600dk have rank \(0\).

Complex multiplication

The elliptic curves in class 321600dk do not have complex multiplication.

Modular form 321600.2.a.dk

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{7} + q^{9} - 6 q^{11} + 2 q^{13} + 3 q^{17} - q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.