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Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 690.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
690.c1 690c2 [1, 1, 0, -3172057, -2148591611] [2] 34560  
690.c2 690c1 [1, 1, 0, -22777, -90852059] [2] 17280 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 690.2.a.c

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

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.