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Properties

Label 296450.ek
Number of curves $2$
Conductor $296450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ek1")
 
E.isogeny_class()
 

Elliptic curves in class 296450.ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
296450.ek1 296450ek2 \([1, 1, 0, -683575, -217819125]\) \(6352571665/2\) \(11121507031250\) \([]\) \(3265920\) \(1.8649\)  
296450.ek2 296450ek1 \([1, 1, 0, -9825, -197875]\) \(18865/8\) \(44486028125000\) \([]\) \(1088640\) \(1.3156\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 296450.ek have rank \(0\).

Complex multiplication

The elliptic curves in class 296450.ek do not have complex multiplication.

Modular form 296450.2.a.ek

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.