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Properties

Label 11466.k
Number of curves $2$
Conductor $11466$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 11466.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11466.k1 11466x2 \([1, -1, 0, -1620452745, -25107048552713]\) \(-5486773802537974663600129/2635437714\) \(-226031269866887394\) \([]\) \(3161088\) \(3.5688\)  
11466.k2 11466x1 \([1, -1, 0, 314865, -768440723]\) \(40251338884511/2997011332224\) \(-257042036557894783104\) \([]\) \(451584\) \(2.5959\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11466.k have rank \(0\).

Complex multiplication

The elliptic curves in class 11466.k do not have complex multiplication.

Modular form 11466.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 5 q^{11} + q^{13} + q^{16} - 3 q^{17} + q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.