Properties

Label 212160.ek
Number of curves $2$
Conductor $212160$
CM no
Rank $1$
Graph

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

Elliptic curves in class 212160.ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
212160.ek1 212160fl1 \([0, 1, 0, -871681, 309383519]\) \(279419703685750081/3666124800000\) \(961052619571200000\) \([2]\) \(2949120\) \(2.2583\) \(\Gamma_0(N)\)-optimal
212160.ek2 212160fl2 \([0, 1, 0, -134401, 816779615]\) \(-1024222994222401/1098922500000000\) \(-288075939840000000000\) \([2]\) \(5898240\) \(2.6048\)  

Rank

sage: E.rank()
 

The elliptic curves in class 212160.ek have rank \(1\).

Complex multiplication

The elliptic curves in class 212160.ek do not have complex multiplication.

Modular form 212160.2.a.ek

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2 q^{7} + q^{9} + q^{13} - q^{15} - q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.