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Properties

Label 16905.d
Number of curves $2$
Conductor $16905$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 16905.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16905.d1 16905h1 \([1, 1, 1, -11271, 391068]\) \(1345938541921/203765625\) \(23972822015625\) \([2]\) \(36864\) \(1.2913\) \(\Gamma_0(N)\)-optimal
16905.d2 16905h2 \([1, 1, 1, 19354, 2179568]\) \(6814692748079/21258460125\) \(-2501036575246125\) \([2]\) \(73728\) \(1.6379\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16905.d have rank \(1\).

Complex multiplication

The elliptic curves in class 16905.d do not have complex multiplication.

Modular form 16905.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3 q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + 4 q^{13} + q^{15} - q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.