Properties

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

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 690.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
690.i1 690i2 \([1, 0, 0, -786, -5940]\) \(53706380371489/16171875000\) \(16171875000\) \([2]\) \(480\) \(0.66410\)  
690.i2 690i1 \([1, 0, 0, 134, -604]\) \(265971760991/317400000\) \(-317400000\) \([2]\) \(240\) \(0.31753\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 690.2.a.i

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