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Properties

Label 364650.k
Number of curves $2$
Conductor $364650$
CM no
Rank $1$
Graph

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

Elliptic curves in class 364650.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.k1 364650k2 \([1, 1, 0, -22685875, 41578880875]\) \(82636196626770537345841/2183420321789850\) \(34115942527966406250\) \([2]\) \(22708224\) \(2.8535\)  
364650.k2 364650k1 \([1, 1, 0, -1362625, 702210625]\) \(-17907429170521685521/3292181367506460\) \(-51440333867288437500\) \([2]\) \(11354112\) \(2.5070\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 364650.k have rank \(1\).

Complex multiplication

The elliptic curves in class 364650.k do not have complex multiplication.

Modular form 364650.2.a.k

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