Properties

Label 16830.t
Number of curves 4
Conductor 16830
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16830.t1")
sage: E.isogeny_class()

Elliptic curves in class 16830.t

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.t1 16830z3 [1, -1, 0, -760374, -255014892] 2 163840  
16830.t2 16830z4 [1, -1, 0, -72054, 571860] 2 163840  
16830.t3 16830z2 [1, -1, 0, -47574, -3966732] 4 81920  
16830.t4 16830z1 [1, -1, 0, -1494, -123660] 2 40960 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

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

Modular form 16830.2.a.t

sage: E.q_eigenform(10)
\( q - q^{2} + q^{4} + q^{5} - 4q^{7} - q^{8} - q^{10} - q^{11} - 2q^{13} + 4q^{14} + q^{16} - q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.