Properties

Label 22848.bz
Number of curves $2$
Conductor $22848$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.bz1 22848ct2 \([0, 1, 0, -1073889, -425939553]\) \(1044942448578893426/7759962920241\) \(1017113859881828352\) \([2]\) \(540672\) \(2.2859\)  
22848.bz2 22848ct1 \([0, 1, 0, -24129, -15063489]\) \(-23707171994692/1480419781911\) \(-97020790827319296\) \([2]\) \(270336\) \(1.9393\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.bz

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2q^{5} + q^{7} + q^{9} + 6q^{11} - 4q^{13} - 2q^{15} - q^{17} + 2q^{19} + O(q^{20})\)  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.