Properties

Label 630.b
Number of curves $6$
Conductor $630$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("630.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 630.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.b1 630d5 [1, -1, 0, -151200, 22667386] [2] 2048  
630.b2 630d4 [1, -1, 0, -9450, 355936] [2, 2] 1024  
630.b3 630d6 [1, -1, 0, -8820, 404950] [2] 2048  
630.b4 630d3 [1, -1, 0, -3330, -69080] [2] 1024  
630.b5 630d2 [1, -1, 0, -630, 4900] [2, 2] 512  
630.b6 630d1 [1, -1, 0, 90, 436] [2] 256 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 630.b have rank \(1\).

Modular form 630.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} + q^{7} - q^{8} + q^{10} - 4q^{11} - 2q^{13} - q^{14} + q^{16} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.