Properties

Label 16900j
Number of curves 4
Conductor 16900
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16900.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16900j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16900.p3 16900j1 [0, -1, 0, -5633, 113762] [2] 27648 \(\Gamma_0(N)\)-optimal
16900.p4 16900j2 [0, -1, 0, 15492, 747512] [2] 55296  
16900.p1 16900j3 [0, -1, 0, -174633, -28024738] [2] 82944  
16900.p2 16900j4 [0, -1, 0, -153508, -35080488] [2] 165888  

Rank

sage: E.rank()
 

The elliptic curves in class 16900j have rank \(0\).

Modular form 16900.2.a.p

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.