Properties

Label 16830.l
Number of curves 6
Conductor 16830
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16830.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16830.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.l1 16830t5 [1, -1, 0, -2629260, 1641423766] [2] 393216  
16830.l2 16830t3 [1, -1, 0, -179010, 20828416] [2, 2] 196608  
16830.l3 16830t2 [1, -1, 0, -66510, -6329084] [2, 2] 98304  
16830.l4 16830t1 [1, -1, 0, -65790, -6478700] [2] 49152 \(\Gamma_0(N)\)-optimal
16830.l5 16830t4 [1, -1, 0, 34470, -23919800] [2] 196608  
16830.l6 16830t6 [1, -1, 0, 471240, 136963066] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 16830.l have rank \(1\).

Modular form 16830.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + q^{11} + 6q^{13} + q^{16} - q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.