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Properties

Label 45177.j
Number of curves $2$
Conductor $45177$
CM no
Rank $1$
Graph

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

Elliptic curves in class 45177.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
45177.j1 45177j2 \([1, 0, 1, -271091, -54347875]\) \(858729462625/40293\) \(103380814197837\) \([2]\) \(218880\) \(1.7635\)  
45177.j2 45177j1 \([1, 0, 1, -17826, -757001]\) \(244140625/45177\) \(115911821979393\) \([2]\) \(109440\) \(1.4169\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 45177.j have rank \(1\).

Complex multiplication

The elliptic curves in class 45177.j do not have complex multiplication.

Modular form 45177.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{6} - 3 q^{8} + q^{9} + q^{11} - q^{12} - 4 q^{13} - q^{16} - 2 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.