Properties

Label 510.g
Number of curves $4$
Conductor $510$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("510.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 510.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
510.g1 510g4 [1, 0, 0, -52405, -4621873] [2] 864  
510.g2 510g3 [1, 0, 0, -3275, -72435] [2] 432  
510.g3 510g2 [1, 0, 0, -655, -6223] [6] 288  
510.g4 510g1 [1, 0, 0, 25, -375] [6] 144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 510.g have rank \(0\).

Modular form 510.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} + q^{10} + q^{12} - 4q^{13} + 2q^{14} + q^{15} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.