Properties

Label 10608x
Number of curves $2$
Conductor $10608$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 10608x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10608.l2 10608x1 \([0, 1, 0, -4200, 103284]\) \(2000852317801/2094417\) \(8578732032\) \([2]\) \(18432\) \(0.82332\) \(\Gamma_0(N)\)-optimal
10608.l1 10608x2 \([0, 1, 0, -5240, 47124]\) \(3885442650361/1996623837\) \(8178171236352\) \([2]\) \(36864\) \(1.1699\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10608x have rank \(2\).

Complex multiplication

The elliptic curves in class 10608x do not have complex multiplication.

Modular form 10608.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{5} - 2 q^{7} + q^{9} - 6 q^{11} - q^{13} - 4 q^{15} + q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.