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Properties

Label 2352n
Number of curves $2$
Conductor $2352$
CM no
Rank $1$
Graph

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

Elliptic curves in class 2352n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2352.j2 2352n1 \([0, -1, 0, -457, -2960]\) \(16384/3\) \(1936973136\) \([2]\) \(1344\) \(0.50060\) \(\Gamma_0(N)\)-optimal
2352.j1 2352n2 \([0, -1, 0, -2172, 36828]\) \(109744/9\) \(92974710528\) \([2]\) \(2688\) \(0.84717\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2352n have rank \(1\).

Complex multiplication

The elliptic curves in class 2352n do not have complex multiplication.

Modular form 2352.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} + q^{9} - 2 q^{11} - 4 q^{13} - 2 q^{15} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.