Properties

Label 3630.z
Number of curves $2$
Conductor $3630$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3630.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3630.z1 3630x1 [1, 0, 0, -166680, -26196048] [2] 21120 \(\Gamma_0(N)\)-optimal
3630.z2 3630x2 [1, 0, 0, -140060, -34836900] [2] 42240  

Rank

sage: E.rank()
 

The elliptic curves in class 3630.z have rank \(0\).

Complex multiplication

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

Modular form 3630.2.a.z

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

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.