Properties

Label 56550.c
Number of curves $2$
Conductor $56550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 56550.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.c1 56550p2 \([1, 1, 0, -3070, 58900]\) \(25612374554333/2305900896\) \(288237612000\) \([2]\) \(122880\) \(0.93853\)  
56550.c2 56550p1 \([1, 1, 0, -670, -5900]\) \(266716895453/45167616\) \(5645952000\) \([2]\) \(61440\) \(0.59195\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 56550.c have rank \(1\).

Complex multiplication

The elliptic curves in class 56550.c do not have complex multiplication.

Modular form 56550.2.a.c

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