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Properties

Label 16830cg
Number of curves $2$
Conductor $16830$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 16830cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16830.bo1 16830cg1 \([1, -1, 1, -923, -10753]\) \(-119168121961/2524500\) \(-1840360500\) \([]\) \(11520\) \(0.56819\) \(\Gamma_0(N)\)-optimal
16830.bo2 16830cg2 \([1, -1, 1, 3802, -50443]\) \(8339492177639/6277634880\) \(-4576395827520\) \([3]\) \(34560\) \(1.1175\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 16830cg do not have complex multiplication.

Modular form 16830.2.a.cg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + q^{11} - q^{13} - q^{14} + q^{16} + q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.