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Properties

Label 465.b
Number of curves $2$
Conductor $465$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 465.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
465.b1 465a2 \([1, 1, 0, -162, 729]\) \(474734543401/564975\) \(564975\) \([2]\) \(96\) \(0.014967\)  
465.b2 465a1 \([1, 1, 0, -7, 16]\) \(-47045881/129735\) \(-129735\) \([2]\) \(48\) \(-0.33161\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 465.b have rank \(1\).

Complex multiplication

The elliptic curves in class 465.b do not have complex multiplication.

Modular form 465.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2 q^{7} - 3 q^{8} + q^{9} + q^{10} - 4 q^{11} + q^{12} - 2 q^{14} - q^{15} - q^{16} + 2 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.