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Properties

Label 144150ey
Number of curves $2$
Conductor $144150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("ey1")
 
E.isogeny_class()
 

Elliptic curves in class 144150ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
144150.z2 144150ey1 \([1, 1, 0, -985525, 385868125]\) \(-7633736209/230640\) \(-3198341390403750000\) \([2]\) \(3686400\) \(2.3286\) \(\Gamma_0(N)\)-optimal
144150.z1 144150ey2 \([1, 1, 0, -15881025, 24352727625]\) \(31942518433489/27900\) \(386896135935937500\) \([2]\) \(7372800\) \(2.6751\)  

Rank

sage: E.rank()
 

The elliptic curves in class 144150ey have rank \(0\).

Complex multiplication

The elliptic curves in class 144150ey do not have complex multiplication.

Modular form 144150.2.a.ey

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.