Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.d1 22050bv2 \([1, -1, 0, -3864492, -3092833584]\) \(-7620530425/526848\) \(-441266692545000000000\) \([]\) \(1244160\) \(2.7123\)  
22050.d2 22050bv1 \([1, -1, 0, 269883, -4455459]\) \(2595575/1512\) \(-1266390380390625000\) \([]\) \(414720\) \(2.1630\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22050.2.a.d

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 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.