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Properties

Label 430950ek
Number of curves $2$
Conductor $430950$
CM no
Rank $0$
Graph

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

Elliptic curves in class 430950ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.ek1 430950ek1 \([1, 0, 1, -115626, 14277148]\) \(4980061835533/313344000\) \(10756512000000000\) \([2]\) \(4644864\) \(1.8273\) \(\Gamma_0(N)\)-optimal
430950.ek2 430950ek2 \([1, 0, 1, 92374, 60037148]\) \(2539391358707/46818000000\) \(-1607174156250000000\) \([2]\) \(9289728\) \(2.1739\)  

Rank

sage: E.rank()
 

The elliptic curves in class 430950ek have rank \(0\).

Complex multiplication

The elliptic curves in class 430950ek do not have complex multiplication.

Modular form 430950.2.a.ek

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 4 q^{7} - q^{8} + q^{9} - 4 q^{11} + q^{12} - 4 q^{14} + q^{16} + q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.