Properties

Label 9800d
Number of curves $4$
Conductor $9800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 9800d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9800.u4 9800d1 [0, 0, 0, 1225, -85750] [2] 12288 \(\Gamma_0(N)\)-optimal
9800.u3 9800d2 [0, 0, 0, -23275, -1286250] [2, 2] 24576  
9800.u1 9800d3 [0, 0, 0, -366275, -85321250] [2] 49152  
9800.u2 9800d4 [0, 0, 0, -72275, 5916750] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 9800d have rank \(0\).

Complex multiplication

The elliptic curves in class 9800d do not have complex multiplication.

Modular form 9800.2.a.d

sage: E.q_eigenform(10)
 
\( q - 3q^{9} - 4q^{11} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.