Properties

Label 630.a
Number of curves 8
Conductor 630
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("630.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 630.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.a1 630c7 [1, -1, 0, -17287200, 27669604050] [2] 16384  
630.a2 630c5 [1, -1, 0, -1080450, 432540000] [2, 2] 8192  
630.a3 630c8 [1, -1, 0, -1073700, 438205950] [2] 16384  
630.a4 630c3 [1, -1, 0, -135630, -19186524] [2] 4096  
630.a5 630c4 [1, -1, 0, -67950, 6682500] [2, 2] 4096  
630.a6 630c2 [1, -1, 0, -9630, -210924] [2, 2] 2048  
630.a7 630c1 [1, -1, 0, 1890, -24300] [2] 1024 \(\Gamma_0(N)\)-optimal
630.a8 630c6 [1, -1, 0, 11430, 21304296] [2] 8192  

Rank

sage: E.rank()
 

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

Modular form 630.2.a.a

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.