Properties

Label 226512.k
Number of curves $2$
Conductor $226512$
CM no
Rank $0$
Graph

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

Elliptic curves in class 226512.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
226512.k1 226512ei1 \([0, 0, 0, -709302, -216014645]\) \(1909913257984/129730653\) \(2680687727151260112\) \([2]\) \(5376000\) \(2.2846\) \(\Gamma_0(N)\)-optimal
226512.k2 226512ei2 \([0, 0, 0, 613833, -929184410]\) \(77366117936/1172914587\) \(-387784094587741133568\) \([2]\) \(10752000\) \(2.6312\)  

Rank

sage: E.rank()
 

The elliptic curves in class 226512.k have rank \(0\).

Complex multiplication

The elliptic curves in class 226512.k do not have complex multiplication.

Modular form 226512.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.