Properties

Label 3630.a
Number of curves $4$
Conductor $3630$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 3630.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3630.a1 3630c3 \([1, 1, 0, -221781628, 1271089482832]\) \(680995599504466943307169/52207031250000000\) \(92487940488281250000000\) \([2]\) \(1075200\) \(3.4550\)  
3630.a2 3630c2 \([1, 1, 0, -14784508, 17059530448]\) \(201738262891771037089/45727545600000000\) \(81009136410681600000000\) \([2, 2]\) \(537600\) \(3.1084\)  
3630.a3 3630c1 \([1, 1, 0, -4872188, -3912956208]\) \(7220044159551112609/448454983680000\) \(794465359343124480000\) \([2]\) \(268800\) \(2.7619\) \(\Gamma_0(N)\)-optimal
3630.a4 3630c4 \([1, 1, 0, 33615492, 105466970448]\) \(2371297246710590562911/4084000833203280000\) \(-7235056600070435920080000\) \([2]\) \(1075200\) \(3.4550\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3630.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.