Properties

Label 9600.d
Number of curves $2$
Conductor $9600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 9600.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9600.d1 9600k2 \([0, -1, 0, -1833, -23463]\) \(42592/9\) \(144000000000\) \([2]\) \(12800\) \(0.85570\)  
9600.d2 9600k1 \([0, -1, 0, -583, 5287]\) \(43904/3\) \(1500000000\) \([2]\) \(6400\) \(0.50912\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9600.d have rank \(0\).

Complex multiplication

The elliptic curves in class 9600.d do not have complex multiplication.

Modular form 9600.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4 q^{7} + q^{9} + 6 q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.