Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10626.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10626.s1 10626q2 \([1, 0, 0, -62068, 5946650]\) \(26444015547214434625/46191222\) \(46191222\) \([2]\) \(21504\) \(1.1586\)  
10626.s2 10626q1 \([1, 0, 0, -3878, 92736]\) \(-6449916994998625/8532911772\) \(-8532911772\) \([2]\) \(10752\) \(0.81201\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10626.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} - q^{11} + q^{12} + 6 q^{13} + q^{14} + q^{16} + 4 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\)  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.