Properties

Label 22848.g
Number of curves $2$
Conductor $22848$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.g1 22848by2 \([0, -1, 0, -23329, -23327]\) \(42852953779784/24786408969\) \(812201049096192\) \([2]\) \(92160\) \(1.5504\)  
22848.g2 22848by1 \([0, -1, 0, 5831, -5831]\) \(5352028359488/3098832471\) \(-12692817801216\) \([2]\) \(46080\) \(1.2038\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.g

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.