Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.cm1 22848co4 \([0, 1, 0, -2177, 34815]\) \(17418812548/1753941\) \(114946277376\) \([2]\) \(20480\) \(0.85845\)  
22848.cm2 22848co2 \([0, 1, 0, -497, -3825]\) \(830321872/127449\) \(2088124416\) \([2, 2]\) \(10240\) \(0.51187\)  
22848.cm3 22848co1 \([0, 1, 0, -477, -4173]\) \(11745974272/357\) \(365568\) \([2]\) \(5120\) \(0.16530\) \(\Gamma_0(N)\)-optimal
22848.cm4 22848co3 \([0, 1, 0, 863, -19873]\) \(1083360092/3306177\) \(-216673615872\) \([2]\) \(20480\) \(0.85845\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.cm

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