↑

Properties

Label 22218l
Number of curves $2$
Conductor $22218$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 22218l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22218.l2 22218l1 \([1, 0, 1, -2664320, -1673768050]\) \(50489872297/12096\) \(501095079640298304\) \([]\) \(556416\) \(2.3856\) \(\Gamma_0(N)\)-optimal
22218.l1 22218l2 \([1, 0, 1, -6861935, 4689816290]\) \(862551551257/269746176\) \(11174642984902936756224\) \([]\) \(1669248\) \(2.9349\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22218l have rank \(1\).

Complex multiplication

The elliptic curves in class 22218l do not have complex multiplication.

Modular form 22218.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{10} + q^{12} - 4 q^{13} + q^{14} - 3 q^{15} + q^{16} + 3 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.