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Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 16830.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16830.a1 16830d1 \([1, -1, 0, -249330, -47842924]\) \(63486961018176728187/21521824913600\) \(581089272667200\) \([2]\) \(153600\) \(1.8049\) \(\Gamma_0(N)\)-optimal
16830.a2 16830d2 \([1, -1, 0, -214650, -61652500]\) \(-40509209135606968827/37479578548445000\) \(-1011948620808015000\) \([2]\) \(307200\) \(2.1515\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16830.2.a.a

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