Properties

Label 9610.a
Number of curves $2$
Conductor $9610$
CM no
Rank $1$
Graph

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

Elliptic curves in class 9610.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9610.a1 9610b2 \([1, 0, 0, -1024446, 399014140]\) \(133974081659809/192200\) \(170578207488200\) \([2]\) \(92160\) \(2.0019\)  
9610.a2 9610b1 \([1, 0, 0, -63446, 6349540]\) \(-31824875809/1240000\) \(-1100504564440000\) \([2]\) \(46080\) \(1.6554\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9610.a have rank \(1\).

Complex multiplication

The elliptic curves in class 9610.a do not have complex multiplication.

Modular form 9610.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.