Properties

Label 4704.n
Number of curves $2$
Conductor $4704$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4704.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.n1 4704e2 \([0, -1, 0, -14177, -373743]\) \(1906624/729\) \(120495224844288\) \([2]\) \(10752\) \(1.4011\)  
4704.n2 4704e1 \([0, -1, 0, -12462, -531180]\) \(82881856/27\) \(69731032896\) \([2]\) \(5376\) \(1.0545\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4704.n have rank \(0\).

Complex multiplication

The elliptic curves in class 4704.n do not have complex multiplication.

Modular form 4704.2.a.n

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