Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22848.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.f1 22848bz4 \([0, -1, 0, -169729, 26970433]\) \(16502300582616584/331494849\) \(10862423212032\) \([4]\) \(114688\) \(1.6219\)  
22848.f2 22848bz3 \([0, -1, 0, -44289, -3171231]\) \(293204888234504/35857918593\) \(1174992276455424\) \([2]\) \(114688\) \(1.6219\)  
22848.f3 22848bz2 \([0, -1, 0, -10969, 394009]\) \(35637273157312/4552605729\) \(18647473065984\) \([2, 2]\) \(57344\) \(1.2753\)  
22848.f4 22848bz1 \([0, -1, 0, 1036, 31458]\) \(1919569026752/7938130977\) \(-508040382528\) \([2]\) \(28672\) \(0.92877\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22848.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{5} - q^{7} + q^{9} - 4q^{11} + 2q^{13} + 2q^{15} + q^{17} - 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.