Properties

Label 150858.o
Number of curves $2$
Conductor $150858$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 150858.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
150858.o1 150858bh2 \([1, -1, 0, -1183509, 499226841]\) \(-10418796526321/82044596\) \(-1443680323732773396\) \([]\) \(2496000\) \(2.3131\)  
150858.o2 150858bh1 \([1, -1, 0, 12951, -945459]\) \(13651919/29696\) \(-522539362538496\) \([]\) \(499200\) \(1.5084\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 150858.o have rank \(0\).

Complex multiplication

The elliptic curves in class 150858.o do not have complex multiplication.

Modular form 150858.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} - 3 q^{11} - q^{13} - 2 q^{14} + q^{16} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.