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Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 10626p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10626.r2 10626p1 \([1, 0, 0, -376363693, -2810465601199]\) \(-5895856113332931416918127084625/215771481613620039647232\) \(-215771481613620039647232\) \([3]\) \(2993760\) \(3.5652\) \(\Gamma_0(N)\)-optimal
10626.r1 10626p2 \([1, 0, 0, -30485726893, -2048771311274671]\) \(-3133382230165522315000208250857964625/153574604080128\) \(-153574604080128\) \([]\) \(8981280\) \(4.1145\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10626.2.a.p

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