Properties

Label 54150.k
Number of curves $2$
Conductor $54150$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 54150.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.k1 54150c2 \([1, 1, 0, -644525, 198868125]\) \(276288773643091/41990400\) \(4500189900000000\) \([2]\) \(491520\) \(2.0161\)  
54150.k2 54150c1 \([1, 1, 0, -36525, 3700125]\) \(-50284268371/26542080\) \(-2844564480000000\) \([2]\) \(245760\) \(1.6695\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54150.k have rank \(1\).

Complex multiplication

The elliptic curves in class 54150.k do not have complex multiplication.

Modular form 54150.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 2 q^{7} - q^{8} + q^{9} - q^{12} + 2 q^{13} - 2 q^{14} + q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.