Properties

Label 630.e
Number of curves 2
Conductor 630
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("630.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 630.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
630.e1 630b1 [1, -1, 0, -5124, 142160] [2] 1120 \(\Gamma_0(N)\)-optimal
630.e2 630b2 [1, -1, 0, -3204, 248528] [2] 2240  

Rank

sage: E.rank()
 

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

Modular form 630.2.a.e

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - 4q^{11} + 6q^{13} + q^{14} + q^{16} + 4q^{17} + 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.