Properties

Label 630.d
Number of curves $4$
Conductor $630$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 630.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
630.d1 630e4 \([1, -1, 0, -2409, 46115]\) \(2121328796049/120050\) \(87516450\) \([2]\) \(512\) \(0.58829\)  
630.d2 630e3 \([1, -1, 0, -789, -7777]\) \(74565301329/5468750\) \(3986718750\) \([2]\) \(512\) \(0.58829\)  
630.d3 630e2 \([1, -1, 0, -159, 665]\) \(611960049/122500\) \(89302500\) \([2, 2]\) \(256\) \(0.24172\)  
630.d4 630e1 \([1, -1, 0, 21, 53]\) \(1367631/2800\) \(-2041200\) \([2]\) \(128\) \(-0.10485\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 630.2.a.d

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.