Properties

Label 22848.bt
Number of curves $2$
Conductor $22848$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.bt1 22848x2 \([0, 1, 0, -3531169, 2552810687]\) \(18575453384550358633/352517816448\) \(92410430474944512\) \([2]\) \(516096\) \(2.3791\)  
22848.bt2 22848x1 \([0, 1, 0, -213409, 42593471]\) \(-4100379159705193/626805817344\) \(-164313384181825536\) \([2]\) \(258048\) \(2.0325\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{5} - q^{7} + q^{9} + 6q^{11} - 2q^{15} - q^{17} + 2q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.