Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.z1 22848bt4 \([0, -1, 0, -506497, -119621183]\) \(438536015880092936/64602489661101\) \(2116894381214957568\) \([2]\) \(294912\) \(2.2411\)  
22848.z2 22848bt2 \([0, -1, 0, -136057, 17515705]\) \(68003243639904448/7163272192041\) \(29340762898599936\) \([2, 2]\) \(147456\) \(1.8946\)  
22848.z3 22848bt1 \([0, -1, 0, -132412, 18589522]\) \(4011705594213827392/52680152007\) \(3371529728448\) \([2]\) \(73728\) \(1.5480\) \(\Gamma_0(N)\)-optimal
22848.z4 22848bt3 \([0, -1, 0, 176063, 85869985]\) \(18419405270942584/108003564029403\) \(-3539060786115477504\) \([2]\) \(294912\) \(2.2411\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.z

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.