Properties

Label 4560.bc
Number of curves $2$
Conductor $4560$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.bc1 4560ba2 \([0, 1, 0, -480, 3828]\) \(2992209121/54150\) \(221798400\) \([2]\) \(2304\) \(0.39672\)  
4560.bc2 4560ba1 \([0, 1, 0, 0, 180]\) \(-1/3420\) \(-14008320\) \([2]\) \(1152\) \(0.050147\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4560.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 4560.bc do not have complex multiplication.

Modular form 4560.2.a.bc

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2 q^{7} + q^{9} + 6 q^{13} + q^{15} + 8 q^{17} - q^{19} + O(q^{20})\)  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 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.