Properties

Label 22848bc
Number of curves $4$
Conductor $22848$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.cp4 22848bc1 \([0, 1, 0, 63, 51615]\) \(103823/4386816\) \(-1149977493504\) \([2]\) \(36864\) \(0.99312\) \(\Gamma_0(N)\)-optimal
22848.cp3 22848bc2 \([0, 1, 0, -20417, 1096095]\) \(3590714269297/73410624\) \(19244154617856\) \([2, 2]\) \(73728\) \(1.3397\)  
22848.cp2 22848bc3 \([0, 1, 0, -43457, -1857633]\) \(34623662831857/14438442312\) \(3784951021436928\) \([2]\) \(147456\) \(1.6863\)  
22848.cp1 22848bc4 \([0, 1, 0, -325057, 71224223]\) \(14489843500598257/6246072\) \(1637370298368\) \([4]\) \(147456\) \(1.6863\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22848bc have rank \(1\).

Complex multiplication

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

Modular form 22848.2.a.bc

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