Properties

Label 1610.a
Number of curves $2$
Conductor $1610$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1610.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1610.a1 1610a2 \([1, -1, 0, -15610, -746700]\) \(420676324562824569/56350000000\) \(56350000000\) \([2]\) \(2688\) \(1.0820\)  
1610.a2 1610a1 \([1, -1, 0, -890, -13644]\) \(-78013216986489/37918720000\) \(-37918720000\) \([2]\) \(1344\) \(0.73538\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1610.a have rank \(1\).

Complex multiplication

The elliptic curves in class 1610.a do not have complex multiplication.

Modular form 1610.2.a.a

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