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Properties

Label 6690j
Number of curves $2$
Conductor $6690$
CM no
Rank $0$
Graph

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

Elliptic curves in class 6690j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6690.j2 6690j1 \([1, 0, 0, -6800, 240000]\) \(-34773983355859201/4877010000000\) \(-4877010000000\) \([7]\) \(19992\) \(1.1659\) \(\Gamma_0(N)\)-optimal
6690.j1 6690j2 \([1, 0, 0, -226250, -60187290]\) \(-1280824409818832580001/822726139895701410\) \(-822726139895701410\) \([]\) \(139944\) \(2.1389\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6690j have rank \(0\).

Complex multiplication

The elliptic curves in class 6690j do not have complex multiplication.

Modular form 6690.2.a.j

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.