Properties

Label 465690bw
Number of curves $2$
Conductor $465690$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 465690bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
465690.bw2 465690bw1 \([1, 1, 1, -13545, -412905]\) \(5841725401/1857600\) \(87392428545600\) \([2]\) \(1886976\) \(1.3790\) \(\Gamma_0(N)\)-optimal*
465690.bw1 465690bw2 \([1, 1, 1, -85745, 9319655]\) \(1481933914201/53916840\) \(2536565238536040\) \([2]\) \(3773952\) \(1.7255\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 465690bw1.

Rank

sage: E.rank()
 

The elliptic curves in class 465690bw have rank \(0\).

Complex multiplication

The elliptic curves in class 465690bw do not have complex multiplication.

Modular form 465690.2.a.bw

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} - 2q^{11} - q^{12} + 2q^{13} - 2q^{14} - q^{15} + q^{16} - 4q^{17} + q^{18} + O(q^{20})\)  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.