Properties

Label 4800.n
Number of curves $2$
Conductor $4800$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.n1 4800bu2 \([0, -1, 0, -673, 4417]\) \(2060602/729\) \(11943936000\) \([2]\) \(3072\) \(0.63477\)  
4800.n2 4800bu1 \([0, -1, 0, 127, 417]\) \(27436/27\) \(-221184000\) \([2]\) \(1536\) \(0.28820\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4800.n have rank \(1\).

Complex multiplication

The elliptic curves in class 4800.n do not have complex multiplication.

Modular form 4800.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} + 2q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.