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Properties

Label 169050ed
Number of curves $2$
Conductor $169050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 169050ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.gp2 169050ed1 \([1, 1, 1, -15338, 1316531]\) \(-217081801/285660\) \(-525118958437500\) \([2]\) \(995328\) \(1.5174\) \(\Gamma_0(N)\)-optimal
169050.gp1 169050ed2 \([1, 1, 1, -297088, 62174531]\) \(1577505447721/838350\) \(1541109986718750\) \([2]\) \(1990656\) \(1.8640\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169050ed have rank \(0\).

Complex multiplication

The elliptic curves in class 169050ed do not have complex multiplication.

Modular form 169050.2.a.ed

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 2 q^{11} - q^{12} + 4 q^{13} + q^{16} - 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.