Properties

Label 3600.n
Number of curves $2$
Conductor $3600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 3600.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3600.n1 3600u2 [0, 0, 0, -1515, -14150] [2] 3072  
3600.n2 3600u1 [0, 0, 0, 285, -1550] [2] 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3600.n have rank \(1\).

Complex multiplication

The elliptic curves in class 3600.n do not have complex multiplication.

Modular form 3600.2.a.n

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

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.