Properties

Label 22848.i
Number of curves $2$
Conductor $22848$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.i1 22848i2 \([0, -1, 0, -89, 249]\) \(19248832/6069\) \(24858624\) \([2]\) \(4608\) \(0.12311\)  
22848.i2 22848i1 \([0, -1, 0, 16, 18]\) \(6644672/7497\) \(-479808\) \([2]\) \(2304\) \(-0.22346\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.i

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