Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 56550.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.bi1 56550bk1 \([1, 1, 1, -20813, 974531]\) \(63812982460681/10201800960\) \(159403140000000\) \([2]\) \(184320\) \(1.4476\) \(\Gamma_0(N)\)-optimal
56550.bi2 56550bk2 \([1, 1, 1, 37187, 5498531]\) \(363979050334199/1041836936400\) \(-16278702131250000\) \([2]\) \(368640\) \(1.7942\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 56550.2.a.bi

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