Properties

Label 630.j
Number of curves 4
Conductor 630
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("630.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 630.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.j1 630h3 [1, -1, 1, -947, -10961] [2] 288  
630.j2 630h4 [1, -1, 1, -677, -17549] [2] 576  
630.j3 630h1 [1, -1, 1, -47, 119] [6] 96 \(\Gamma_0(N)\)-optimal
630.j4 630h2 [1, -1, 1, 73, 551] [6] 192  

Rank

sage: E.rank()
 

The elliptic curves in class 630.j have rank \(0\).

Modular form 630.2.a.j

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 2q^{13} + q^{14} + q^{16} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.