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Properties

Label 10626f
Number of curves $2$
Conductor $10626$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 10626f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10626.j1 10626f1 \([1, 0, 1, -2327, 43058]\) \(-1392658229178217/2225976984\) \(-2225976984\) \([3]\) \(10368\) \(0.69132\) \(\Gamma_0(N)\)-optimal
10626.j2 10626f2 \([1, 0, 1, 3538, 207968]\) \(4899746835008423/21466897503744\) \(-21466897503744\) \([]\) \(31104\) \(1.2406\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10626f have rank \(0\).

Complex multiplication

The elliptic curves in class 10626f do not have complex multiplication.

Modular form 10626.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - 3 q^{10} - q^{11} + q^{12} - q^{13} - q^{14} + 3 q^{15} + q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.