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Properties

Label 1650.q
Number of curves $2$
Conductor $1650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 1650.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1650.q1 1650r1 \([1, 0, 0, -578, 5412]\) \(-854307420745/20785248\) \(-519631200\) \([5]\) \(1200\) \(0.45782\) \(\Gamma_0(N)\)-optimal
1650.q2 1650r2 \([1, 0, 0, 3112, -246858]\) \(341297975/2898918\) \(-28309746093750\) \([]\) \(6000\) \(1.2625\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1650.q have rank \(0\).

Complex multiplication

The elliptic curves in class 1650.q do not have complex multiplication.

Modular form 1650.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{11} + q^{12} - q^{13} - 2 q^{14} + q^{16} + 8 q^{17} + q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.