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Properties

Label 17787.k
Number of curves $2$
Conductor $17787$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 17787.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17787.k1 17787i2 \([1, 1, 1, -430823, -67411618]\) \(14553591673375/5208653241\) \(3165014301887765943\) \([2]\) \(307200\) \(2.2508\)  
17787.k2 17787i1 \([1, 1, 1, 81612, -7354236]\) \(98931640625/96059601\) \(-58370176882856223\) \([2]\) \(153600\) \(1.9042\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17787.k have rank \(1\).

Complex multiplication

The elliptic curves in class 17787.k do not have complex multiplication.

Modular form 17787.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 3 q^{8} + q^{9} + q^{12} - 4 q^{13} - q^{16} + 4 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) 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.