Properties

Label 690j
Number of curves $2$
Conductor $690$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 690j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
690.j2 690j1 \([1, 0, 0, -245, -1503]\) \(-1626794704081/8125440\) \(-8125440\) \([2]\) \(240\) \(0.17333\) \(\Gamma_0(N)\)-optimal
690.j1 690j2 \([1, 0, 0, -3925, -94975]\) \(6687281588245201/165600\) \(165600\) \([2]\) \(480\) \(0.51991\)  

Rank

sage: E.rank()
 

The elliptic curves in class 690j have rank \(0\).

Complex multiplication

The elliptic curves in class 690j do not have complex multiplication.

Modular form 690.2.a.j

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