Properties

Label 16224.o
Number of curves $2$
Conductor $16224$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 16224.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16224.o1 16224u1 \([0, 1, 0, -490494, -132345108]\) \(42246001231552/14414517\) \(4452871704720192\) \([2]\) \(129024\) \(1.9743\) \(\Gamma_0(N)\)-optimal
16224.o2 16224u2 \([0, 1, 0, -422049, -170523729]\) \(-420526439488/390971529\) \(-7729745489596256256\) \([2]\) \(258048\) \(2.3208\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16224.o have rank \(1\).

Complex multiplication

The elliptic curves in class 16224.o do not have complex multiplication.

Modular form 16224.2.a.o

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - 2 q^{7} + q^{9} + 2 q^{11} - 2 q^{15} + 6 q^{17} - 2 q^{19} + O(q^{20})\) Copy content 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.