Properties

Label 185150.j
Number of curves $2$
Conductor $185150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 185150.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185150.j1 185150bu2 \([1, 1, 0, -2345, 42745]\) \(107906079985/1372\) \(18144700\) \([]\) \(103680\) \(0.53875\)  
185150.j2 185150bu1 \([1, 1, 0, -45, -35]\) \(788785/448\) \(5924800\) \([]\) \(34560\) \(-0.010554\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 185150.j have rank \(1\).

Complex multiplication

The elliptic curves in class 185150.j do not have complex multiplication.

Modular form 185150.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + q^{7} - q^{8} - 2 q^{9} - q^{12} - 2 q^{13} - q^{14} + q^{16} + 6 q^{17} + 2 q^{18} + 7 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.