Properties

Label 9900k
Number of curves 2
Conductor 9900
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9900.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9900k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9900.w2 9900k1 [0, 0, 0, 600, 3125] [2] 6144 \(\Gamma_0(N)\)-optimal
9900.w1 9900k2 [0, 0, 0, -2775, 26750] [2] 12288  

Rank

sage: E.rank()
 

The elliptic curves in class 9900k have rank \(1\).

Modular form 9900.2.a.w

sage: E.q_eigenform(10)
 
\( q + 2q^{7} - q^{11} + 2q^{13} + 4q^{17} - 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.