↑

Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 510.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
510.d1 510c2 \([1, 1, 1, -156, 603]\) \(420021471169/50191650\) \(50191650\) \([2]\) \(160\) \(0.20855\)  
510.d2 510c1 \([1, 1, 1, 14, 59]\) \(302111711/1404540\) \(-1404540\) \([2]\) \(80\) \(-0.13802\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 510.d do not have complex multiplication.

Modular form 510.2.a.d

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

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.