Properties

Label 22848.ct
Number of curves $2$
Conductor $22848$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.ct1 22848bm2 \([0, 1, 0, -24417, 1460223]\) \(6141556990297/1019592\) \(267279925248\) \([2]\) \(36864\) \(1.2006\)  
22848.ct2 22848bm1 \([0, 1, 0, -1377, 27135]\) \(-1102302937/616896\) \(-161715585024\) \([2]\) \(18432\) \(0.85405\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.ct

sage: E.q_eigenform(10)
 
\(q + q^{3} + 2q^{5} + q^{7} + q^{9} + 2q^{11} - 4q^{13} + 2q^{15} + q^{17} + 2q^{19} + O(q^{20})\)  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.