Properties

Label 510.a
Number of curves $2$
Conductor $510$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("510.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 510.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
510.a1 510a2 [1, 1, 0, -46193, 3801813] [2] 2016  
510.a2 510a1 [1, 1, 0, -2673, 67797] [2] 1008 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 510.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 4q^{13} - 2q^{14} + q^{15} + q^{16} + q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.