Properties

Label 3525.k
Number of curves $2$
Conductor $3525$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3525.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3525.k1 3525j2 \([1, 0, 1, -3576, -82577]\) \(323535264625/59643\) \(931921875\) \([2]\) \(3456\) \(0.72369\)  
3525.k2 3525j1 \([1, 0, 1, -201, -1577]\) \(-57066625/34263\) \(-535359375\) \([2]\) \(1728\) \(0.37712\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3525.k have rank \(0\).

Complex multiplication

The elliptic curves in class 3525.k do not have complex multiplication.

Modular form 3525.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} - 4q^{7} - 3q^{8} + q^{9} - q^{12} - 6q^{13} - 4q^{14} - q^{16} + 6q^{17} + q^{18} + 2q^{19} + O(q^{20})\)  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.