Properties

Label 3630.g
Number of curves $2$
Conductor $3630$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3630.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3630.g1 3630i2 [1, 0, 1, -1939, -32914] [] 2592  
3630.g2 3630i1 [1, 0, 1, -124, 482] [3] 864 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3630.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + q^{12} - q^{13} + q^{14} - q^{15} + q^{16} - 3q^{17} - q^{18} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.