Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("630.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 630e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.d4 630e1 [1, -1, 0, 21, 53] [2] 128 \(\Gamma_0(N)\)-optimal
630.d3 630e2 [1, -1, 0, -159, 665] [2, 2] 256  
630.d2 630e3 [1, -1, 0, -789, -7777] [2] 512  
630.d1 630e4 [1, -1, 0, -2409, 46115] [2] 512  

Rank

sage: E.rank()
 

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

Modular form 630.2.a.d

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

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 Cremona 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 Cremona labels.