Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 54150z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.t1 54150z1 \([1, 0, 1, -27435286, -55318180312]\) \(-14899652746105/1492992\) \(-228840821859170764800\) \([]\) \(4333824\) \(2.9408\) \(\Gamma_0(N)\)-optimal
54150.t2 54150z2 \([1, 0, 1, 1886939, -165616661872]\) \(4847542295/77309411328\) \(-11849728080088979944243200\) \([]\) \(13001472\) \(3.4901\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 54150.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 2 q^{7} - q^{8} + q^{9} - 3 q^{11} + q^{12} + 2 q^{13} + 2 q^{14} + q^{16} - 3 q^{17} - q^{18} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.