Properties

Label 10626e
Number of curves $2$
Conductor $10626$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 10626e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10626.g1 10626e1 \([1, 0, 1, -8401, 295652]\) \(-65560514292015625/149954112\) \(-149954112\) \([3]\) \(14688\) \(0.81262\) \(\Gamma_0(N)\)-optimal
10626.g2 10626e2 \([1, 0, 1, -5776, 484190]\) \(-21305767155765625/89149883547648\) \(-89149883547648\) \([]\) \(44064\) \(1.3619\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10626e have rank \(1\).

Complex multiplication

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

Modular form 10626.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} - q^{11} + q^{12} + 5 q^{13} - q^{14} + q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) 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.