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Properties

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

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Show commands: SageMath
E = EllipticCurve("if1")
 
E.isogeny_class()
 

Elliptic curves in class 169050if

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.p2 169050if1 \([1, 1, 0, 4875, -1177875]\) \(6967871/331200\) \(-608833575000000\) \([2]\) \(829440\) \(1.5166\) \(\Gamma_0(N)\)-optimal
169050.p1 169050if2 \([1, 1, 0, -142125, -19846875]\) \(172715635009/7935000\) \(14586637734375000\) \([2]\) \(1658880\) \(1.8632\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 169050.2.a.if

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