Properties

Label 1650q
Number of curves $4$
Conductor $1650$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1650q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1650.r3 1650q1 \([1, 0, 0, -34838, -2505708]\) \(299270638153369/1069200\) \(16706250000\) \([2]\) \(3840\) \(1.1796\) \(\Gamma_0(N)\)-optimal
1650.r2 1650q2 \([1, 0, 0, -35338, -2430208]\) \(312341975961049/17862322500\) \(279098789062500\) \([2, 2]\) \(7680\) \(1.5261\)  
1650.r1 1650q3 \([1, 0, 0, -104088, 9876042]\) \(7981893677157049/1917731420550\) \(29964553446093750\) \([2]\) \(15360\) \(1.8727\)  
1650.r4 1650q4 \([1, 0, 0, 25412, -9902458]\) \(116149984977671/2779502343750\) \(-43429724121093750\) \([2]\) \(15360\) \(1.8727\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1650.2.a.q

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.