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Properties

Label 22050.f
Number of curves $2$
Conductor $22050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 22050.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.f1 22050cw2 \([1, -1, 0, -32293242, -70626217334]\) \(266916252066900625/162\) \(2260469531250\) \([]\) \(1036800\) \(2.5932\)  
22050.f2 22050cw1 \([1, -1, 0, -399492, -96378584]\) \(505318200625/4251528\) \(59323762378125000\) \([]\) \(345600\) \(2.0439\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22050.f have rank \(0\).

Complex multiplication

The elliptic curves in class 22050.f do not have complex multiplication.

Modular form 22050.2.a.f

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.