Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("630.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 630.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.h1 630i7 [1, -1, 1, -3161093, 2164026557] [6] 9216  
630.h2 630i6 [1, -1, 1, -197573, 33848381] [2, 6] 4608  
630.h3 630i8 [1, -1, 1, -183173, 38980541] [6] 9216  
630.h4 630i4 [1, -1, 1, -39218, 2946557] [2] 3072  
630.h5 630i3 [1, -1, 1, -13253, 449597] [6] 2304  
630.h6 630i2 [1, -1, 1, -5198, -74419] [2, 2] 1536  
630.h7 630i1 [1, -1, 1, -4478, -114163] [2] 768 \(\Gamma_0(N)\)-optimal
630.h8 630i5 [1, -1, 1, 17302, -560419] [2] 3072  

Rank

sage: E.rank()
 

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

Modular form 630.2.a.h

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.