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Properties

Label 215950.k
Number of curves $2$
Conductor $215950$
CM no
Rank $1$
Graph

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

Elliptic curves in class 215950.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215950.k1 215950u1 \([1, -1, 0, -6167, 83741]\) \(1660218096321/773964800\) \(12093200000000\) \([2]\) \(376320\) \(1.2048\) \(\Gamma_0(N)\)-optimal
215950.k2 215950u2 \([1, -1, 0, 21833, 615741]\) \(73660174154559/53296460000\) \(-832757187500000\) \([2]\) \(752640\) \(1.5513\)  

Rank

sage: E.rank()
 

The elliptic curves in class 215950.k have rank \(1\).

Complex multiplication

The elliptic curves in class 215950.k do not have complex multiplication.

Modular form 215950.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} - 2 q^{13} - q^{14} + q^{16} - 4 q^{17} + 3 q^{18} + 4 q^{19} + O(q^{20})\) 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.