Properties

Label 22848.bb
Number of curves $4$
Conductor $22848$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.bb1 22848h4 \([0, -1, 0, -725469697, 7521266762497]\) \(322159999717985454060440834/4250799\) \(557160726528\) \([4]\) \(2211840\) \(3.2376\)  
22848.bb2 22848h3 \([0, -1, 0, -45458497, 116896156993]\) \(79260902459030376659234/842751810121431609\) \(110461165256236283854848\) \([2]\) \(2211840\) \(3.2376\)  
22848.bb3 22848h2 \([0, -1, 0, -45341857, 117531121825]\) \(157304700372188331121828/18069292138401\) \(1184189129582247936\) \([2, 2]\) \(1105920\) \(2.8910\)  
22848.bb4 22848h1 \([0, -1, 0, -2826577, 1847044945]\) \(-152435594466395827792/1646846627220711\) \(-26981935140384129024\) \([2]\) \(552960\) \(2.5444\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22848.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 22848.bb do not have complex multiplication.

Modular form 22848.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{5} - q^{7} + q^{9} - 2q^{13} - 2q^{15} + q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.