Properties

Label 627.a
Number of curves 2
Conductor 627
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("627.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 627.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
627.a1 627b2 [0, 1, 1, -30063, -2016358] [] 540  
627.a2 627b1 [0, 1, 1, -363, -2995] [3] 180 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 627.a have rank \(0\).

Modular form 627.2.a.a

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{4} + 2q^{7} + q^{9} + q^{11} - 2q^{12} - q^{13} + 4q^{16} + 3q^{17} + q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.