Properties

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

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 3630.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3630.v1 3630u2 \([1, 0, 0, -234561, 43573641]\) \(55025549689/192000\) \(4979985523392000\) \([]\) \(28512\) \(1.8746\)  
3630.v2 3630u1 \([1, 0, 0, -14946, -656820]\) \(14235529/1080\) \(28012418569080\) \([]\) \(9504\) \(1.3253\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3630.2.a.v

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