Properties

Label 22050fu
Number of curves $2$
Conductor $22050$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("fu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050fu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.cz2 22050fu1 \([1, -1, 1, 10795, -37803]\) \(2595575/1512\) \(-81048984345000\) \([]\) \(82944\) \(1.3583\) \(\Gamma_0(N)\)-optimal
22050.cz1 22050fu2 \([1, -1, 1, -154580, -24711753]\) \(-7620530425/526848\) \(-28241068322880000\) \([]\) \(248832\) \(1.9076\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22050fu have rank \(1\).

Complex multiplication

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

Modular form 22050.2.a.fu

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.