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Properties

Label 328560.bb
Number of curves $2$
Conductor $328560$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 328560.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
328560.bb1 328560bb2 \([0, -1, 0, -161301845000, 24934925098394352]\) \(-44164307457093068844199489/1823508000000000\) \(-19163638303222874112000000000\) \([]\) \(780088320\) \(4.9133\)  
328560.bb2 328560bb1 \([0, -1, 0, -1826706440, 40095333327600]\) \(-64144540676215729729/28962038218752000\) \(-304368297231643956926742528000\) \([]\) \(260029440\) \(4.3640\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 328560.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 328560.bb do not have complex multiplication.

Modular form 328560.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} - 3 q^{11} - 2 q^{13} - q^{15} - 3 q^{17} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.