Properties

Label 3630.n
Number of curves $4$
Conductor $3630$
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 3630.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3630.n1 3630n3 [1, 1, 1, -503786, -105462367] [2] 76800  
3630.n2 3630n2 [1, 1, 1, -171036, 25774233] [2, 2] 38400  
3630.n3 3630n1 [1, 1, 1, -168616, 26579609] [4] 19200 \(\Gamma_0(N)\)-optimal
3630.n4 3630n4 [1, 1, 1, 122994, 105515169] [2] 76800  

Rank

sage: E.rank()
 

The elliptic curves in class 3630.n have rank \(1\).

Complex multiplication

The elliptic curves in class 3630.n do not have complex multiplication.

Modular form 3630.2.a.n

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - q^{12} - 2q^{13} + q^{15} + q^{16} + 2q^{17} + q^{18} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.