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Properties

Label 363166.k
Number of curves $2$
Conductor $363166$
CM no
Rank $0$
Graph

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

Elliptic curves in class 363166.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363166.k1 363166k2 \([1, -1, 1, -11620, -106625]\) \(3687953625/2024072\) \(95224250447432\) \([2]\) \(898128\) \(1.3729\)  
363166.k2 363166k1 \([1, -1, 1, 2820, -14209]\) \(52734375/32192\) \(-1514501001152\) \([2]\) \(449064\) \(1.0264\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 363166.k have rank \(0\).

Complex multiplication

The elliptic curves in class 363166.k do not have complex multiplication.

Modular form 363166.2.a.k

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.