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Properties

Label 209814r
Number of curves $2$
Conductor $209814$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 209814r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
209814.dj1 209814r1 \([1, 0, 0, -88151, -6402747]\) \(1771561/612\) \(26169839635627908\) \([2]\) \(3317760\) \(1.8520\) \(\Gamma_0(N)\)-optimal
209814.dj2 209814r2 \([1, 0, 0, 261539, -44518957]\) \(46268279/46818\) \(-2001992732125534962\) \([2]\) \(6635520\) \(2.1986\)  

Rank

sage: E.rank()
 

The elliptic curves in class 209814r have rank \(0\).

Complex multiplication

The elliptic curves in class 209814r do not have complex multiplication.

Modular form 209814.2.a.r

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} - 2 q^{7} + q^{8} + q^{9} + 4 q^{10} + q^{12} + 6 q^{13} - 2 q^{14} + 4 q^{15} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.