Properties

Label 22218.bi
Number of curves $2$
Conductor $22218$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 22218.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22218.bi1 22218be2 \([1, 0, 0, -14294, 3001002]\) \(-2181825073/25039686\) \(-3706772177290854\) \([]\) \(190080\) \(1.6693\)  
22218.bi2 22218be1 \([1, 0, 0, 1576, -106344]\) \(2924207/34776\) \(-5148096075864\) \([]\) \(63360\) \(1.1200\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22218.bi have rank \(0\).

Complex multiplication

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

Modular form 22218.2.a.bi

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