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Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 3630.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3630.u1 3630v2 \([1, 0, 0, -1738591, -644446879]\) \(2711280982499089/732421875000\) \(157001133544921875000\) \([]\) \(142560\) \(2.5833\)  
3630.u2 3630v1 \([1, 0, 0, -620551, 188045705]\) \(123286270205329/43200000\) \(9260303659200000\) \([3]\) \(47520\) \(2.0340\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3630.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.