Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 630.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.i1 630j3 [1, -1, 1, -3362, -74181] [2] 512  
630.i2 630j2 [1, -1, 1, -212, -1101] [2, 2] 256  
630.i3 630j1 [1, -1, 1, -32, 51] [4] 128 \(\Gamma_0(N)\)-optimal
630.i4 630j4 [1, -1, 1, 58, -3909] [2] 512  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 630.i do not have complex multiplication.

Modular form 630.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} + 4q^{11} - 2q^{13} - q^{14} + q^{16} + 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.